%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP397_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:12:48 AM UTC 2025
% Result : Theorem 0.82s 0.99s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP397_1 : TPTP v9.0.0. Released v8.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 18:48:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.82/0.99 % SZS status Theorem
% 0.82/0.99 % SZS output start Proof
% 0.82/0.99 tff(tptp_fun__fun_app_c__type, type, (
% 0.82/0.99 tptp_fun__fun_app_c_: ( |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'| * |'A_ell2_a_ell2_cblinfun$'| ) > |'C_ell2_c_ell2_cblinfun$'|)).
% 0.82/0.99 tff(tptp_fun_A__questionmark_v4_73_type, type, (
% 0.82/0.99 tptp_fun_A__questionmark_v4_73: ( |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'| * |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'| * |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| ) > |'A_ell2_a_ell2_cblinfun$'|)).
% 0.82/0.99 tff(tptp_fun__i___type, type, (
% 0.82/0.99 tptp_fun__i__: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__comp_k__type, type, (
% 0.82/0.99 tptp_fun__comp_k_: ( |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'| * |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| ) > |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__j___type, type, (
% 0.82/0.99 tptp_fun__j__: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__g___type, type, (
% 0.82/0.99 tptp_fun__g__: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun_A__questionmark_v1_117_type, type, (
% 0.82/0.99 tptp_fun_A__questionmark_v1_117: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| > |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__fun_app_a__type, type, (
% 0.82/0.99 tptp_fun__fun_app_a_: ( |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_b_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun_fun$'| * |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| ) > |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__comp___type, type, (
% 0.82/0.99 tptp_fun__comp__: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'| > |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_b_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__f___type, type, (
% 0.82/0.99 tptp_fun__f__: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__fun_app_b__type, type, (
% 0.82/0.99 tptp_fun__fun_app_b_: ( |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'| * |'B_ell2_b_ell2_cblinfun$'| ) > |'C_ell2_c_ell2_cblinfun$'|)).
% 0.82/0.99 tff(tptp_fun__fun_app_n__type, type, (
% 0.82/0.99 tptp_fun__fun_app_n_: ( |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| * |'C_ell2_c_ell2_cblinfun$'| ) > |'B_ell2_b_ell2_cblinfun$'|)).
% 0.82/0.99 tff(tptp_fun__inv_into_a__type, type, (
% 0.82/0.99 tptp_fun__inv_into_a_: ( |'B_ell2_b_ell2_cblinfun_set$'| * |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'| ) > |'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun_A__questionmark_v1_116_type, type, (
% 0.82/0.99 tptp_fun_A__questionmark_v1_116: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| > |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__collect_b__type, type, (
% 0.82/0.99 tptp_fun__collect_b_: |'B_ell2_b_ell2_cblinfun_bool_fun$'| > |'B_ell2_b_ell2_cblinfun_set$'|)).
% 0.82/0.99 tff(tptp_fun__top_d__type, type, (
% 0.82/0.99 tptp_fun__top_d_: |'B_ell2_b_ell2_cblinfun_bool_fun$'|)).
% 0.82/0.99 tff(tptp_fun__member___type, type, (
% 0.82/0.99 tptp_fun__member__: ( |'C_ell2_c_ell2_cblinfun$'| * |'C_ell2_c_ell2_cblinfun_set$'| ) > $o)).
% 0.82/0.99 tff(tptp_fun__image_a__type, type, (
% 0.82/0.99 tptp_fun__image_a_: ( |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'| * |'B_ell2_b_ell2_cblinfun_set$'| ) > |'C_ell2_c_ell2_cblinfun_set$'|)).
% 0.82/0.99 tff(tptp_fun__image___type, type, (
% 0.82/0.99 tptp_fun__image__: ( |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'| * |'A_ell2_a_ell2_cblinfun_set$'| ) > |'C_ell2_c_ell2_cblinfun_set$'|)).
% 0.82/0.99 tff(tptp_fun__top___type, type, (
% 0.82/0.99 tptp_fun__top__: |'A_ell2_a_ell2_cblinfun_set$'|)).
% 0.82/0.99 tff(tptp_fun__collect_a__type, type, (
% 0.82/0.99 tptp_fun__collect_a_: |'A_ell2_a_ell2_cblinfun_bool_fun$'| > |'A_ell2_a_ell2_cblinfun_set$'|)).
% 0.82/0.99 tff(tptp_fun__top_c__type, type, (
% 0.82/0.99 tptp_fun__top_c_: |'A_ell2_a_ell2_cblinfun_bool_fun$'|)).
% 0.82/0.99 tff(tptp_fun__comp_n__type, type, (
% 0.82/0.99 tptp_fun__comp_n_: ( |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'| * |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| ) > |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__id_a__type, type, (
% 0.82/0.99 tptp_fun__id_a_: |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__fun_app_i__type, type, (
% 0.82/0.99 tptp_fun__fun_app_i_: ( |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_a_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_fun$'| * |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| ) > |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__comp_b__type, type, (
% 0.82/0.99 tptp_fun__comp_b_: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| > |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_a_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__clinear_c__type, type, (
% 0.82/0.99 tptp_fun__clinear_c_: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| > $o)).
% 0.82/0.99 tff(tptp_fun__image_e__type, type, (
% 0.82/0.99 tptp_fun__image_e_: ( |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| * |'B_ell2_b_ell2_cblinfun_set$'| ) > |'A_ell2_a_ell2_cblinfun_set$'|)).
% 0.82/0.99 tff(tptp_fun__top_a__type, type, (
% 0.82/0.99 tptp_fun__top_a_: |'B_ell2_b_ell2_cblinfun_set$'|)).
% 0.82/0.99 tff(tptp_fun__inv_into_c__type, type, (
% 0.82/0.99 tptp_fun__inv_into_c_: ( |'B_ell2_b_ell2_cblinfun_set$'| * |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| ) > |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__iso_register___type, type, (
% 0.82/0.99 tptp_fun__iso_register__: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| > $o)).
% 0.82/0.99 tff(tptp_fun__clinear_b__type, type, (
% 0.82/0.99 tptp_fun__clinear_b_: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| > $o)).
% 0.82/0.99 tff(tptp_fun__register_b__type, type, (
% 0.82/0.99 tptp_fun__register_b_: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| > $o)).
% 0.82/0.99 tff(tptp_fun__fun_app_o__type, type, (
% 0.82/0.99 tptp_fun__fun_app_o_: ( |'A_ell2_a_ell2_cblinfun_set_a_ell2_a_ell2_cblinfun_set_fun$'| * |'A_ell2_a_ell2_cblinfun_set$'| ) > |'A_ell2_a_ell2_cblinfun_set$'|)).
% 0.82/0.99 tff(tptp_fun__image_c__type, type, (
% 0.82/0.99 tptp_fun__image_c_: |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| > |'A_ell2_a_ell2_cblinfun_set_a_ell2_a_ell2_cblinfun_set_fun$'|)).
% 0.82/0.99 tff(tptp_fun__fun_app_p__type, type, (
% 0.82/0.99 tptp_fun__fun_app_p_: ( |'B_ell2_b_ell2_cblinfun_set_b_ell2_b_ell2_cblinfun_set_fun$'| * |'B_ell2_b_ell2_cblinfun_set$'| ) > |'B_ell2_b_ell2_cblinfun_set$'|)).
% 0.82/0.99 tff(tptp_fun__image_d__type, type, (
% 0.82/0.99 tptp_fun__image_d_: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| > |'B_ell2_b_ell2_cblinfun_set_b_ell2_b_ell2_cblinfun_set_fun$'|)).
% 0.82/0.99 tff(tptp_fun__id___type, type, (
% 0.82/0.99 tptp_fun__id__: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__comp_j__type, type, (
% 0.82/0.99 tptp_fun__comp_j_: ( |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'| * |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| ) > |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__fun_app_f__type, type, (
% 0.82/0.99 tptp_fun__fun_app_f_: ( |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_b_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_fun$'| * |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| ) > |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__comp_a__type, type, (
% 0.82/0.99 tptp_fun__comp_a_: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| > |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_b_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__image_f__type, type, (
% 0.82/0.99 tptp_fun__image_f_: ( |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| * |'A_ell2_a_ell2_cblinfun_set$'| ) > |'B_ell2_b_ell2_cblinfun_set$'|)).
% 0.82/0.99 tff(tptp_fun__inv_into_b__type, type, (
% 0.82/0.99 tptp_fun__inv_into_b_: ( |'A_ell2_a_ell2_cblinfun_set$'| * |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| ) > |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__iso_register_e__type, type, (
% 0.82/0.99 tptp_fun__iso_register_e_: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| > $o)).
% 0.82/0.99 tff(tptp_fun__register_c__type, type, (
% 0.82/0.99 tptp_fun__register_c_: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| > $o)).
% 0.82/0.99 tff(tptp_fun__inj_on_f__type, type, (
% 0.82/0.99 tptp_fun__inj_on_f_: ( |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| * |'A_ell2_a_ell2_cblinfun_set$'| ) > $o)).
% 0.82/0.99 tff(tptp_fun__inj_on_e__type, type, (
% 0.82/0.99 tptp_fun__inj_on_e_: ( |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| * |'B_ell2_b_ell2_cblinfun_set$'| ) > $o)).
% 0.82/0.99 tff(tptp_fun__comp_h__type, type, (
% 0.82/0.99 tptp_fun__comp_h_: ( |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| * |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| ) > |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun_A__questionmark_v1_118_type, type, (
% 0.82/0.99 tptp_fun_A__questionmark_v1_118: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| > |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__comp_l__type, type, (
% 0.82/0.99 tptp_fun__comp_l_: ( |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| * |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| ) > |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__clinear_d__type, type, (
% 0.82/0.99 tptp_fun__clinear_d_: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| > $o)).
% 0.82/0.99 tff(tptp_fun_A__questionmark_v1_107_type, type, (
% 0.82/0.99 tptp_fun_A__questionmark_v1_107: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| > |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__register_d__type, type, (
% 0.82/0.99 tptp_fun__register_d_: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| > $o)).
% 0.82/0.99 tff(tptp_fun__iso_register_f__type, type, (
% 0.82/0.99 tptp_fun__iso_register_f_: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| > $o)).
% 0.82/0.99 tff(tptp_fun__inv_into_g__type, type, (
% 0.82/0.99 tptp_fun__inv_into_g_: ( |'B_ell2_b_ell2_cblinfun_set$'| * |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| ) > |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun__fun_app_d__type, type, (
% 0.82/0.99 tptp_fun__fun_app_d_: ( |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| * |'B_ell2_b_ell2_cblinfun$'| ) > |'A_ell2_a_ell2_cblinfun$'|)).
% 0.82/0.99 tff(tptp_fun__fun_app_g__type, type, (
% 0.82/0.99 tptp_fun__fun_app_g_: ( |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| * |'A_ell2_a_ell2_cblinfun$'| ) > |'B_ell2_b_ell2_cblinfun$'|)).
% 0.82/0.99 tff(tptp_fun_A__questionmark_v1_123_type, type, (
% 0.82/0.99 tptp_fun_A__questionmark_v1_123: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| > |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|)).
% 0.82/0.99 tff(tptp_fun_A__questionmark_v2_97_type, type, (
% 0.82/0.99 tptp_fun_A__questionmark_v2_97: ( |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| * |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| ) > |'B_ell2_b_ell2_cblinfun$'|)).
% 0.82/0.99 tff(tptp_fun_A__questionmark_v2_51_type, type, (
% 0.82/0.99 tptp_fun_A__questionmark_v2_51: ( |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'| * |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'| ) > |'A_ell2_a_ell2_cblinfun$'|)).
% 0.82/0.99 tff(tptp_fun__member_a__type, type, (
% 0.82/0.99 tptp_fun__member_a_: ( |'A_ell2_a_ell2_cblinfun$'| * |'A_ell2_a_ell2_cblinfun_set$'| ) > $o)).
% 0.82/0.99 tff(1,plain,
% 0.82/0.99 ((|'top$'| = tptp_fun__collect_a_(|'top$c'|)) <=> (|'top$'| = tptp_fun__collect_a_(|'top$c'|))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2,axiom,(|'top$'| = tptp_fun__collect_a_(|'top$c'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom167')).
% 0.82/0.99 tff(3,plain,
% 0.82/0.99 (|'top$'| = tptp_fun__collect_a_(|'top$c'|)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.82/0.99 tff(4,plain,
% 0.82/0.99 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : refl(((tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|)) <=> ((tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|)))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(5,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[4])).
% 0.82/0.99 tff(6,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(7,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom517')).
% 0.82/0.99 tff(8,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.82/0.99 tff(9,plain,(
% 0.82/0.99 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))),
% 0.82/0.99 inference(skolemize,[status(sab)],[8])).
% 0.82/0.99 tff(10,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.82/0.99 tff(11,plain,
% 0.82/0.99 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))) | ((tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(|'top$a'|, |'i$'|)) = |'id$a'|))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(12,plain,
% 0.82/0.99 ((tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(|'top$a'|, |'i$'|)) = |'id$a'|)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.82/0.99 tff(13,plain,
% 0.82/0.99 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : refl(((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|)) <=> ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|)))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(14,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[13])).
% 0.82/0.99 tff(15,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(16,plain,
% 0.82/0.99 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : rewrite((tptp_fun__iso_register__(A__questionmark_v0) => (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|)) <=> ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|)))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(17,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register__(A__questionmark_v0) => (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[16])).
% 0.82/0.99 tff(18,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register__(A__questionmark_v0) => (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom543')).
% 0.82/0.99 tff(19,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.82/0.99 tff(20,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.82/0.99 tff(21,plain,(
% 0.82/0.99 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))),
% 0.82/0.99 inference(skolemize,[status(sab)],[20])).
% 0.82/0.99 tff(22,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.82/0.99 tff(23,plain,
% 0.82/0.99 (tptp_fun__iso_register__(|'i$'|) <=> tptp_fun__iso_register__(|'i$'|)),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(24,axiom,(tptp_fun__iso_register__(|'i$'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom4')).
% 0.82/0.99 tff(25,plain,
% 0.82/0.99 (tptp_fun__iso_register__(|'i$'|)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.82/0.99 tff(26,plain,
% 0.82/0.99 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))) | ((~tptp_fun__iso_register__(|'i$'|)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(|'top$a'|, |'i$'|)) = |'id$a'|))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))) | (~tptp_fun__iso_register__(|'i$'|)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(|'top$a'|, |'i$'|)) = |'id$a'|))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(27,plain,
% 0.82/0.99 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))) | ((~tptp_fun__iso_register__(|'i$'|)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(|'top$a'|, |'i$'|)) = |'id$a'|))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(28,plain,
% 0.82/0.99 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0)) = |'id$a'|))) | (~tptp_fun__iso_register__(|'i$'|)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(|'top$a'|, |'i$'|)) = |'id$a'|)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.82/0.99 tff(29,plain,
% 0.82/0.99 (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(|'top$a'|, |'i$'|)) = |'id$a'|),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[28, 25, 22])).
% 0.82/0.99 tff(30,plain,
% 0.82/0.99 ((~((tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(|'top$a'|, |'i$'|)) = |'id$a'|))) | (tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(|'top$a'|, |'i$'|)) = |'id$a'|))),
% 0.82/0.99 inference(tautology,[status(thm)],[])).
% 0.82/0.99 tff(31,plain,
% 0.82/0.99 ((~((tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(|'top$a'|, |'i$'|)) = |'id$a'|))) | (tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.82/0.99 tff(32,plain,
% 0.82/0.99 (tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[31, 12])).
% 0.82/0.99 tff(33,plain,
% 0.82/0.99 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : refl((tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0))) <=> (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(34,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0)))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[33])).
% 0.82/0.99 tff(35,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(36,plain,
% 0.82/0.99 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : rewrite((tptp_fun__register_b_(A__questionmark_v0) => tptp_fun__clinear_b_(A__questionmark_v0)) <=> (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(37,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__register_b_(A__questionmark_v0) => tptp_fun__clinear_b_(A__questionmark_v0)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0)))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[36])).
% 0.82/0.99 tff(38,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__register_b_(A__questionmark_v0) => tptp_fun__clinear_b_(A__questionmark_v0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom56')).
% 0.82/0.99 tff(39,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.82/0.99 tff(40,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.82/0.99 tff(41,plain,(
% 0.82/0.99 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0)))),
% 0.82/0.99 inference(skolemize,[status(sab)],[40])).
% 0.82/0.99 tff(42,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.82/0.99 tff(43,plain,
% 0.82/0.99 (tptp_fun__register_b_(|'i$'|) <=> tptp_fun__register_b_(|'i$'|)),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(44,axiom,(tptp_fun__register_b_(|'i$'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom10')).
% 0.82/0.99 tff(45,plain,
% 0.82/0.99 (tptp_fun__register_b_(|'i$'|)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.82/0.99 tff(46,plain,
% 0.82/0.99 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0)))) | (tptp_fun__clinear_b_(|'i$'|) | (~tptp_fun__register_b_(|'i$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0)))) | tptp_fun__clinear_b_(|'i$'|) | (~tptp_fun__register_b_(|'i$'|)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(47,plain,
% 0.82/0.99 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0)))) | (tptp_fun__clinear_b_(|'i$'|) | (~tptp_fun__register_b_(|'i$'|)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(48,plain,
% 0.82/0.99 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v0)))) | tptp_fun__clinear_b_(|'i$'|) | (~tptp_fun__register_b_(|'i$'|))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.82/0.99 tff(49,plain,
% 0.82/0.99 (tptp_fun__clinear_b_(|'i$'|)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[48, 45, 42])).
% 0.82/0.99 tff(50,plain,
% 0.82/0.99 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : refl(((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|))))) <=> ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|))))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(51,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|))))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[50])).
% 0.82/0.99 tff(52,plain,
% 0.82/0.99 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) <=> (~((~tptp_fun__clinear_b_(A__questionmark_v0)) | (~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))))), ((~(tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) <=> (~(~((~tptp_fun__clinear_b_(A__questionmark_v0)) | (~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))))))), rewrite((~(~((~tptp_fun__clinear_b_(A__questionmark_v0)) | (~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))))) <=> ((~tptp_fun__clinear_b_(A__questionmark_v0)) | (~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)))), ((~(tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) <=> ((~tptp_fun__clinear_b_(A__questionmark_v0)) | (~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))))), rewrite((tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)) <=> (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|))))), (((~(tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) | (tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|))) <=> (((~tptp_fun__clinear_b_(A__questionmark_v0)) | (~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|))))))), rewrite((((~tptp_fun__clinear_b_(A__questionmark_v0)) | (~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|))))) <=> ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))), (((~(tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) | (tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|))) <=> ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(53,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) | (tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[52])).
% 0.82/0.99 tff(54,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) | ?[A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) | ?[A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(55,plain,
% 0.82/0.99 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : rewrite(((tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) => ?[A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|))) <=> ((~(tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) | ?[A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(56,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) => ?[A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) | ?[A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[55])).
% 0.82/0.99 tff(57,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) => ?[A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom521')).
% 0.82/0.99 tff(58,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) | ?[A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.82/0.99 tff(59,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) | ?[A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.82/0.99 tff(60,plain,(
% 0.82/0.99 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_b_(A__questionmark_v0) & (tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|))) | (tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))),
% 0.82/0.99 inference(skolemize,[status(sab)],[59])).
% 0.82/0.99 tff(61,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.82/0.99 tff(62,plain,
% 0.82/0.99 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.82/0.99 tff(63,plain,
% 0.82/0.99 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))) | ((~tptp_fun__clinear_b_(|'i$'|)) | (~(tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(|'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|)))))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))) | (~tptp_fun__clinear_b_(|'i$'|)) | (~(tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(|'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|)))))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(64,plain,
% 0.82/0.99 (((~(tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(|'i$'|)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(|'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|))))) <=> ((~tptp_fun__clinear_b_(|'i$'|)) | (~(tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(|'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|)))))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(65,plain,
% 0.82/0.99 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))) | ((~(tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(|'i$'|)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(|'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|)))))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))) | ((~tptp_fun__clinear_b_(|'i$'|)) | (~(tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(|'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|))))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[64])).
% 0.82/0.99 tff(66,plain,
% 0.82/0.99 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))) | ((~(tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(|'i$'|)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(|'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|)))))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))) | (~tptp_fun__clinear_b_(|'i$'|)) | (~(tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(|'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|)))))),
% 0.82/0.99 inference(transitivity,[status(thm)],[65, 63])).
% 0.82/0.99 tff(67,plain,
% 0.82/0.99 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))) | ((~(tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(|'i$'|)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(|'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|)))))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(68,plain,
% 0.82/0.99 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_e_(A__questionmark_v0, |'top$a'|) = |'top$'|)) | (~tptp_fun__clinear_b_(A__questionmark_v0)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun_A__questionmark_v1_117(A__questionmark_v0)) = |'id$a'|)))))) | (~tptp_fun__clinear_b_(|'i$'|)) | (~(tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(|'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.82/0.99 tff(69,plain,
% 0.82/0.99 ((~(tptp_fun__image_e_(|'i$'|, |'top$a'|) = |'top$'|)) | (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(|'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|))))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[68, 62, 49])).
% 0.82/0.99 tff(70,plain,
% 0.82/0.99 (~((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(|'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|)))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[69, 32])).
% 0.82/0.99 tff(71,plain,
% 0.82/0.99 (((~tptp_fun__clinear_c_(tptp_fun_A__questionmark_v1_117(|'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|))) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|)),
% 0.82/0.99 inference(tautology,[status(thm)],[])).
% 0.82/0.99 tff(72,plain,
% 0.82/0.99 (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = |'id$a'|),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.82/0.99 tff(73,plain,
% 0.82/0.99 (|'id$a'| = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))),
% 0.82/0.99 inference(symmetry,[status(thm)],[72])).
% 0.82/0.99 tff(74,plain,
% 0.82/0.99 (tptp_fun__comp_n_(|'f$'|, |'id$a'|) = tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[73])).
% 0.82/0.99 tff(75,plain,
% 0.82/0.99 (tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))) = tptp_fun__comp_n_(|'f$'|, |'id$a'|)),
% 0.82/0.99 inference(symmetry,[status(thm)],[74])).
% 0.82/0.99 tff(76,plain,
% 0.82/0.99 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl((tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3)) <=> (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3)))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(77,plain,
% 0.82/0.99 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[76])).
% 0.82/0.99 tff(78,plain,
% 0.82/0.99 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(79,plain,
% 0.82/0.99 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/0.99 inference(elim_unused_vars,[status(thm)],[])).
% 0.82/0.99 tff(80,plain,
% 0.82/0.99 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(A__questionmark_v2, A__questionmark_v3))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/0.99 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.82/0.99 tff(81,plain,
% 0.82/0.99 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(A__questionmark_v2, A__questionmark_v3))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/0.99 inference(transitivity,[status(thm)],[80, 79])).
% 0.82/0.99 tff(82,plain,
% 0.82/0.99 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite(((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(A__questionmark_v2, A__questionmark_v3))) <=> ((~(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(A__questionmark_v2, A__questionmark_v3))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(83,plain,
% 0.82/0.99 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(A__questionmark_v2, A__questionmark_v3))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(A__questionmark_v2, A__questionmark_v3)))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[82])).
% 0.82/0.99 tff(84,plain,
% 0.82/0.99 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(A__questionmark_v2, A__questionmark_v3))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/0.99 inference(transitivity,[status(thm)],[83, 81])).
% 0.82/0.99 tff(85,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(A__questionmark_v2, A__questionmark_v3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom625')).
% 0.82/0.99 tff(86,plain,
% 0.82/0.99 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.82/0.99 tff(87,plain,
% 0.82/0.99 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[86, 78])).
% 0.82/0.99 tff(88,plain,(
% 0.82/0.99 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/0.99 inference(skolemize,[status(sab)],[87])).
% 0.82/0.99 tff(89,plain,
% 0.82/0.99 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[88, 77])).
% 0.82/0.99 tff(90,plain,
% 0.82/0.99 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))) | (tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(91,plain,
% 0.82/0.99 (tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.82/0.99 tff(92,plain,
% 0.82/0.99 (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)))),
% 0.82/0.99 inference(symmetry,[status(thm)],[91])).
% 0.82/0.99 tff(93,plain,
% 0.82/0.99 (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)) = tptp_fun__comp_n_(|'f$'|, |'id$a'|)),
% 0.82/0.99 inference(transitivity,[status(thm)],[92, 75])).
% 0.82/0.99 tff(94,plain,
% 0.82/0.99 (tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), |'top$'|) = tptp_fun__image__(tptp_fun__comp_n_(|'f$'|, |'id$a'|), tptp_fun__collect_a_(|'top$c'|))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[93, 3])).
% 0.82/0.99 tff(95,plain,
% 0.82/0.99 (tptp_fun__image__(tptp_fun__comp_n_(|'f$'|, |'id$a'|), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), |'top$'|)),
% 0.82/0.99 inference(symmetry,[status(thm)],[94])).
% 0.82/0.99 tff(96,plain,
% 0.82/0.99 (tptp_fun__image__(tptp_fun__comp_n_(|'f$'|, |'id$a'|), |'top$'|) = tptp_fun__image__(tptp_fun__comp_n_(|'f$'|, |'id$a'|), tptp_fun__collect_a_(|'top$c'|))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[3])).
% 0.82/0.99 tff(97,plain,
% 0.82/0.99 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : refl((tptp_fun__image__(tptp_fun__comp_n_(A__questionmark_v0, A__questionmark_v1), |'top$'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__fun_app_o_(tptp_fun__image_c_(A__questionmark_v1), |'top$'|))) <=> (tptp_fun__image__(tptp_fun__comp_n_(A__questionmark_v0, A__questionmark_v1), |'top$'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__fun_app_o_(tptp_fun__image_c_(A__questionmark_v1), |'top$'|))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(98,plain,
% 0.82/0.99 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__image__(tptp_fun__comp_n_(A__questionmark_v0, A__questionmark_v1), |'top$'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__fun_app_o_(tptp_fun__image_c_(A__questionmark_v1), |'top$'|))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__image__(tptp_fun__comp_n_(A__questionmark_v0, A__questionmark_v1), |'top$'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__fun_app_o_(tptp_fun__image_c_(A__questionmark_v1), |'top$'|)))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[97])).
% 0.82/0.99 tff(99,plain,
% 0.82/0.99 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__image__(tptp_fun__comp_n_(A__questionmark_v0, A__questionmark_v1), |'top$'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__fun_app_o_(tptp_fun__image_c_(A__questionmark_v1), |'top$'|))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__image__(tptp_fun__comp_n_(A__questionmark_v0, A__questionmark_v1), |'top$'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__fun_app_o_(tptp_fun__image_c_(A__questionmark_v1), |'top$'|)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(100,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__image__(tptp_fun__comp_n_(A__questionmark_v0, A__questionmark_v1), |'top$'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__fun_app_o_(tptp_fun__image_c_(A__questionmark_v1), |'top$'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom268')).
% 0.82/0.99 tff(101,plain,
% 0.82/0.99 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__image__(tptp_fun__comp_n_(A__questionmark_v0, A__questionmark_v1), |'top$'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__fun_app_o_(tptp_fun__image_c_(A__questionmark_v1), |'top$'|)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.82/0.99 tff(102,plain,(
% 0.82/0.99 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__image__(tptp_fun__comp_n_(A__questionmark_v0, A__questionmark_v1), |'top$'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__fun_app_o_(tptp_fun__image_c_(A__questionmark_v1), |'top$'|)))),
% 0.82/1.00 inference(skolemize,[status(sab)],[101])).
% 0.82/1.00 tff(103,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__image__(tptp_fun__comp_n_(A__questionmark_v0, A__questionmark_v1), |'top$'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__fun_app_o_(tptp_fun__image_c_(A__questionmark_v1), |'top$'|)))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.82/1.00 tff(104,plain,
% 0.82/1.00 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__image__(tptp_fun__comp_n_(A__questionmark_v0, A__questionmark_v1), |'top$'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__fun_app_o_(tptp_fun__image_c_(A__questionmark_v1), |'top$'|)))) | (tptp_fun__image__(tptp_fun__comp_n_(|'f$'|, |'id$a'|), |'top$'|) = tptp_fun__image__(|'f$'|, tptp_fun__fun_app_o_(tptp_fun__image_c_(|'id$a'|), |'top$'|)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(105,plain,
% 0.82/1.00 (tptp_fun__image__(tptp_fun__comp_n_(|'f$'|, |'id$a'|), |'top$'|) = tptp_fun__image__(|'f$'|, tptp_fun__fun_app_o_(tptp_fun__image_c_(|'id$a'|), |'top$'|))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.82/1.00 tff(106,plain,
% 0.82/1.00 (tptp_fun__image__(|'f$'|, tptp_fun__fun_app_o_(tptp_fun__image_c_(|'id$a'|), |'top$'|)) = tptp_fun__image__(tptp_fun__comp_n_(|'f$'|, |'id$a'|), |'top$'|)),
% 0.82/1.00 inference(symmetry,[status(thm)],[105])).
% 0.82/1.00 tff(107,plain,
% 0.82/1.00 ((tptp_fun__fun_app_o_(tptp_fun__image_c_(|'id$a'|), |'top$'|) = |'top$'|) <=> (tptp_fun__fun_app_o_(tptp_fun__image_c_(|'id$a'|), |'top$'|) = |'top$'|)),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(108,axiom,(tptp_fun__fun_app_o_(tptp_fun__image_c_(|'id$a'|), |'top$'|) = |'top$'|), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom472')).
% 0.82/1.00 tff(109,plain,
% 0.82/1.00 (tptp_fun__fun_app_o_(tptp_fun__image_c_(|'id$a'|), |'top$'|) = |'top$'|),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.82/1.00 tff(110,plain,
% 0.82/1.00 (|'top$'| = tptp_fun__fun_app_o_(tptp_fun__image_c_(|'id$a'|), |'top$'|)),
% 0.82/1.00 inference(symmetry,[status(thm)],[109])).
% 0.82/1.00 tff(111,plain,
% 0.82/1.00 (tptp_fun__image__(|'f$'|, |'top$'|) = tptp_fun__image__(|'f$'|, tptp_fun__fun_app_o_(tptp_fun__image_c_(|'id$a'|), |'top$'|))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[110])).
% 0.82/1.00 tff(112,plain,
% 0.82/1.00 ((tptp_fun__image__(|'f$'|, |'top$'|) = tptp_fun__image_a_(|'g$'|, |'top$a'|)) <=> (tptp_fun__image__(|'f$'|, |'top$'|) = tptp_fun__image_a_(|'g$'|, |'top$a'|))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(113,axiom,(tptp_fun__image__(|'f$'|, |'top$'|) = tptp_fun__image_a_(|'g$'|, |'top$a'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom97')).
% 0.82/1.00 tff(114,plain,
% 0.82/1.00 (tptp_fun__image__(|'f$'|, |'top$'|) = tptp_fun__image_a_(|'g$'|, |'top$a'|)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.82/1.00 tff(115,plain,
% 0.82/1.00 (tptp_fun__image_a_(|'g$'|, |'top$a'|) = tptp_fun__image__(|'f$'|, |'top$'|)),
% 0.82/1.00 inference(symmetry,[status(thm)],[114])).
% 0.82/1.00 tff(116,plain,
% 0.82/1.00 ((tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|) = |'top$a'|) <=> (tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|) = |'top$a'|)),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(117,axiom,(tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|) = |'top$a'|), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom473')).
% 0.82/1.00 tff(118,plain,
% 0.82/1.00 (tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|) = |'top$a'|),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.82/1.00 tff(119,plain,
% 0.82/1.00 (tptp_fun__image_a_(|'g$'|, tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|)) = tptp_fun__image_a_(|'g$'|, |'top$a'|)),
% 0.82/1.00 inference(monotonicity,[status(thm)],[118])).
% 0.82/1.00 tff(120,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl((tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), |'top$a'|) = tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), |'top$a'|))) <=> (tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), |'top$a'|) = tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), |'top$a'|))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(121,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), |'top$a'|) = tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), |'top$a'|))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), |'top$a'|) = tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), |'top$a'|)))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[120])).
% 0.82/1.00 tff(122,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), |'top$a'|) = tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), |'top$a'|))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), |'top$a'|) = tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), |'top$a'|)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(123,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), |'top$a'|) = tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), |'top$a'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom273')).
% 0.82/1.00 tff(124,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), |'top$a'|) = tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), |'top$a'|)))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.82/1.00 tff(125,plain,(
% 0.82/1.00 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), |'top$a'|) = tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), |'top$a'|)))),
% 0.82/1.00 inference(skolemize,[status(sab)],[124])).
% 0.82/1.00 tff(126,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), |'top$a'|) = tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), |'top$a'|)))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.82/1.00 tff(127,plain,
% 0.82/1.00 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), |'top$a'|) = tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), |'top$a'|)))) | (tptp_fun__image_a_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'top$a'|) = tptp_fun__image_a_(|'g$'|, tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(128,plain,
% 0.82/1.00 (tptp_fun__image_a_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'top$a'|) = tptp_fun__image_a_(|'g$'|, tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.82/1.00 tff(129,plain,
% 0.82/1.00 ((|'top$a'| = tptp_fun__collect_b_(|'top$d'|)) <=> (|'top$a'| = tptp_fun__collect_b_(|'top$d'|))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(130,axiom,(|'top$a'| = tptp_fun__collect_b_(|'top$d'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom168')).
% 0.82/1.00 tff(131,plain,
% 0.82/1.00 (|'top$a'| = tptp_fun__collect_b_(|'top$d'|)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.82/1.00 tff(132,plain,
% 0.82/1.00 (tptp_fun__collect_b_(|'top$d'|) = |'top$a'|),
% 0.82/1.00 inference(symmetry,[status(thm)],[131])).
% 0.82/1.00 tff(133,plain,
% 0.82/1.00 (tptp_fun__image_a_(tptp_fun__comp_j_(|'g$'|, |'id$'|), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image_a_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'top$a'|)),
% 0.82/1.00 inference(monotonicity,[status(thm)],[132])).
% 0.82/1.00 tff(134,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl(((tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|)) <=> ((tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|)))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(135,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[134])).
% 0.82/1.00 tff(136,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(137,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom515')).
% 0.82/1.00 tff(138,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.82/1.00 tff(139,plain,(
% 0.82/1.00 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))),
% 0.82/1.00 inference(skolemize,[status(sab)],[138])).
% 0.82/1.00 tff(140,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.82/1.00 tff(141,plain,
% 0.82/1.00 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))) | ((tptp_fun__image_f_(|'j$'|, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)) = |'id$'|))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(142,plain,
% 0.82/1.00 ((tptp_fun__image_f_(|'j$'|, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)) = |'id$'|)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.82/1.00 tff(143,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : refl((tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0))) <=> (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(144,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[143])).
% 0.82/1.00 tff(145,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) <=> (~((~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0))))), ((~(tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) <=> (~(~((~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0))))))), rewrite((~(~((~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0))))) <=> ((~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))), ((~(tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) <=> ((~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0))))), ((tptp_fun__iso_register_e_(A__questionmark_v0) | (~(tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))) <=> (tptp_fun__iso_register_e_(A__questionmark_v0) | ((~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))))), rewrite((tptp_fun__iso_register_e_(A__questionmark_v0) | ((~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))) <=> (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))), ((tptp_fun__iso_register_e_(A__questionmark_v0) | (~(tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))) <=> (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(146,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~(tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[145])).
% 0.82/1.00 tff(147,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~(tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~(tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(148,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : trans(monotonicity(trans(monotonicity(rewrite(((tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) <=> (tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|))), ((((tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) <=> ((tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))), rewrite(((tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) <=> (tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))), ((((tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) <=> (tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))), (((((tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) => tptp_fun__iso_register_e_(A__questionmark_v0)) <=> ((tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) => tptp_fun__iso_register_e_(A__questionmark_v0)))), rewrite(((tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) => tptp_fun__iso_register_e_(A__questionmark_v0)) <=> (tptp_fun__iso_register_e_(A__questionmark_v0) | (~(tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))))), (((((tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) => tptp_fun__iso_register_e_(A__questionmark_v0)) <=> (tptp_fun__iso_register_e_(A__questionmark_v0) | (~(tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(149,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((((tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) => tptp_fun__iso_register_e_(A__questionmark_v0)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~(tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[148])).
% 0.82/1.00 tff(150,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((((tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) => tptp_fun__iso_register_e_(A__questionmark_v0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom510')).
% 0.82/1.00 tff(151,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~(tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.82/1.00 tff(152,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~(tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.82/1.00 tff(153,plain,(
% 0.82/1.00 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~(tptp_fun__register_c_(A__questionmark_v0) & tptp_fun__register_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))))),
% 0.82/1.00 inference(skolemize,[status(sab)],[152])).
% 0.82/1.00 tff(154,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.82/1.00 tff(155,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[154, 144])).
% 0.82/1.00 tff(156,plain,
% 0.82/1.00 ((tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(157,axiom,(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom389')).
% 0.82/1.00 tff(158,plain,
% 0.82/1.00 (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.82/1.00 tff(159,plain,
% 0.82/1.00 ((tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(160,axiom,(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom388')).
% 0.82/1.00 tff(161,plain,
% 0.82/1.00 (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.82/1.00 tff(162,plain,
% 0.82/1.00 (tptp_fun__register_c_(|'j$'|) <=> tptp_fun__register_c_(|'j$'|)),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(163,axiom,(tptp_fun__register_c_(|'j$'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom335')).
% 0.82/1.00 tff(164,plain,
% 0.82/1.00 (tptp_fun__register_c_(|'j$'|)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.82/1.00 tff(165,plain,
% 0.82/1.00 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))) | ((~tptp_fun__register_b_(|'i$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | tptp_fun__iso_register_e_(|'j$'|) | (~tptp_fun__register_c_(|'j$'|)))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))) | (~tptp_fun__register_b_(|'i$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | tptp_fun__iso_register_e_(|'j$'|) | (~tptp_fun__register_c_(|'j$'|)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(166,plain,
% 0.82/1.00 ((tptp_fun__iso_register_e_(|'j$'|) | (~tptp_fun__register_b_(|'i$'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~tptp_fun__register_c_(|'j$'|))) <=> ((~tptp_fun__register_b_(|'i$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | tptp_fun__iso_register_e_(|'j$'|) | (~tptp_fun__register_c_(|'j$'|)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(167,plain,
% 0.82/1.00 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))) | (tptp_fun__iso_register_e_(|'j$'|) | (~tptp_fun__register_b_(|'i$'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~tptp_fun__register_c_(|'j$'|)))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))) | ((~tptp_fun__register_b_(|'i$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | tptp_fun__iso_register_e_(|'j$'|) | (~tptp_fun__register_c_(|'j$'|))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[166])).
% 0.82/1.00 tff(168,plain,
% 0.82/1.00 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))) | (tptp_fun__iso_register_e_(|'j$'|) | (~tptp_fun__register_b_(|'i$'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~tptp_fun__register_c_(|'j$'|)))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))) | (~tptp_fun__register_b_(|'i$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | tptp_fun__iso_register_e_(|'j$'|) | (~tptp_fun__register_c_(|'j$'|)))),
% 0.82/1.00 inference(transitivity,[status(thm)],[167, 165])).
% 0.82/1.00 tff(169,plain,
% 0.82/1.00 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))) | (tptp_fun__iso_register_e_(|'j$'|) | (~tptp_fun__register_b_(|'i$'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~tptp_fun__register_c_(|'j$'|)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(170,plain,
% 0.82/1.00 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) | (~tptp_fun__register_b_(A__questionmark_v1)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) | (~tptp_fun__register_c_(A__questionmark_v0)))) | (~tptp_fun__register_b_(|'i$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | tptp_fun__iso_register_e_(|'j$'|) | (~tptp_fun__register_c_(|'j$'|))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.82/1.00 tff(171,plain,
% 0.82/1.00 (tptp_fun__iso_register_e_(|'j$'|)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[170, 45, 164, 161, 158, 155])).
% 0.82/1.00 tff(172,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl(((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|)) <=> ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|)))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(173,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[172])).
% 0.82/1.00 tff(174,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(175,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite((tptp_fun__iso_register_e_(A__questionmark_v0) => (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|)) <=> ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|)))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(176,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) => (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[175])).
% 0.82/1.00 tff(177,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_e_(A__questionmark_v0) => (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom539')).
% 0.82/1.00 tff(178,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.82/1.00 tff(179,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.82/1.00 tff(180,plain,(
% 0.82/1.00 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))),
% 0.82/1.00 inference(skolemize,[status(sab)],[179])).
% 0.82/1.00 tff(181,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.82/1.00 tff(182,plain,
% 0.82/1.00 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))) | ((~tptp_fun__iso_register_e_(|'j$'|)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)) = |'id$'|))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))) | (~tptp_fun__iso_register_e_(|'j$'|)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)) = |'id$'|))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(183,plain,
% 0.82/1.00 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))) | ((~tptp_fun__iso_register_e_(|'j$'|)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)) = |'id$'|))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(184,plain,
% 0.82/1.00 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__iso_register_e_(A__questionmark_v0)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)) = |'id$'|))) | (~tptp_fun__iso_register_e_(|'j$'|)) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)) = |'id$'|)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.82/1.00 tff(185,plain,
% 0.82/1.00 (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)) = |'id$'|),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[184, 181, 171])).
% 0.82/1.00 tff(186,plain,
% 0.82/1.00 ((~((tptp_fun__image_f_(|'j$'|, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)) = |'id$'|))) | (tptp_fun__image_f_(|'j$'|, |'top$'|) = |'top$a'|) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)) = |'id$'|))),
% 0.82/1.00 inference(tautology,[status(thm)],[])).
% 0.82/1.00 tff(187,plain,
% 0.82/1.00 ((~((tptp_fun__image_f_(|'j$'|, |'top$'|) = |'top$a'|) <=> (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)) = |'id$'|))) | (tptp_fun__image_f_(|'j$'|, |'top$'|) = |'top$a'|)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.82/1.00 tff(188,plain,
% 0.82/1.00 (tptp_fun__image_f_(|'j$'|, |'top$'|) = |'top$a'|),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[187, 142])).
% 0.82/1.00 tff(189,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl((tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0))) <=> (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(190,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[189])).
% 0.82/1.00 tff(191,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(192,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite((tptp_fun__register_c_(A__questionmark_v0) => tptp_fun__clinear_c_(A__questionmark_v0)) <=> (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(193,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__register_c_(A__questionmark_v0) => tptp_fun__clinear_c_(A__questionmark_v0)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[192])).
% 0.82/1.00 tff(194,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__register_c_(A__questionmark_v0) => tptp_fun__clinear_c_(A__questionmark_v0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom57')).
% 0.82/1.00 tff(195,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.82/1.00 tff(196,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[195, 191])).
% 0.82/1.00 tff(197,plain,(
% 0.82/1.00 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 0.82/1.00 inference(skolemize,[status(sab)],[196])).
% 0.82/1.00 tff(198,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[197, 190])).
% 0.82/1.00 tff(199,plain,
% 0.82/1.00 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))) | (tptp_fun__clinear_c_(|'j$'|) | (~tptp_fun__register_c_(|'j$'|)))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))) | tptp_fun__clinear_c_(|'j$'|) | (~tptp_fun__register_c_(|'j$'|)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(200,plain,
% 0.82/1.00 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))) | (tptp_fun__clinear_c_(|'j$'|) | (~tptp_fun__register_c_(|'j$'|)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(201,plain,
% 0.82/1.00 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))) | tptp_fun__clinear_c_(|'j$'|) | (~tptp_fun__register_c_(|'j$'|))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.82/1.00 tff(202,plain,
% 0.82/1.00 (tptp_fun__clinear_c_(|'j$'|)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[201, 198, 164])).
% 0.82/1.00 tff(203,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl(((~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|))))) <=> ((~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|))))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(204,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|))))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|)))))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[203])).
% 0.82/1.00 tff(205,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) <=> (~((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))))), ((~(tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) <=> (~(~((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))))))), rewrite((~(~((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))))) <=> ((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)))), ((~(tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) <=> ((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))))), rewrite((tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|)) <=> (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|))))), (((~(tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) | (tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|))) <=> (((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|))))))), rewrite((((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|))))) <=> ((~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|)))))), (((~(tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) | (tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|))) <=> ((~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|)))))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(206,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) | (tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|)))))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[205])).
% 0.82/1.00 tff(207,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(208,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite(((tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) => ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|))) <=> ((~(tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(209,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) => ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[208])).
% 0.82/1.00 tff(210,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) => ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom520')).
% 0.82/1.00 tff(211,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.82/1.00 tff(212,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.82/1.00 tff(213,plain,(
% 0.82/1.00 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & (tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|))) | (tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|)))),
% 0.82/1.00 inference(skolemize,[status(sab)],[212])).
% 0.82/1.00 tff(214,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|)))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.82/1.00 tff(215,plain,
% 0.82/1.00 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|)))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[214, 204])).
% 0.82/1.00 tff(216,plain,
% 0.82/1.00 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|)))))) | ((~(tptp_fun__image_f_(|'j$'|, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(|'j$'|)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(|'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|)) = |'id$'|)))))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|)))))) | (~(tptp_fun__image_f_(|'j$'|, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(|'j$'|)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(|'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|)) = |'id$'|)))))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(217,plain,
% 0.82/1.00 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|)))))) | ((~(tptp_fun__image_f_(|'j$'|, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(|'j$'|)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(|'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|)) = |'id$'|)))))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(218,plain,
% 0.82/1.00 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__image_f_(A__questionmark_v0, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(A__questionmark_v0))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun_A__questionmark_v1_116(A__questionmark_v0)) = |'id$'|)))))) | (~(tptp_fun__image_f_(|'j$'|, |'top$'|) = |'top$a'|)) | (~tptp_fun__clinear_c_(|'j$'|)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(|'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|)) = |'id$'|))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.82/1.00 tff(219,plain,
% 0.82/1.00 ((~(tptp_fun__image_f_(|'j$'|, |'top$'|) = |'top$a'|)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(|'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|)) = |'id$'|))))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[218, 215, 202])).
% 0.82/1.00 tff(220,plain,
% 0.82/1.00 (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(|'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|)) = |'id$'|)))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[219, 188])).
% 0.82/1.00 tff(221,plain,
% 0.82/1.00 (((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_116(|'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|)) = |'id$'|))) | (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|)) = |'id$'|)),
% 0.82/1.00 inference(tautology,[status(thm)],[])).
% 0.82/1.00 tff(222,plain,
% 0.82/1.00 (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|)) = |'id$'|),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.82/1.00 tff(223,plain,
% 0.82/1.00 (|'id$'| = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|))),
% 0.82/1.00 inference(symmetry,[status(thm)],[222])).
% 0.82/1.00 tff(224,plain,
% 0.82/1.00 (tptp_fun__comp_j_(|'g$'|, |'id$'|) = tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|)))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[223])).
% 0.82/1.00 tff(225,plain,
% 0.82/1.00 (tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|))) = tptp_fun__comp_j_(|'g$'|, |'id$'|)),
% 0.82/1.00 inference(symmetry,[status(thm)],[224])).
% 0.82/1.00 tff(226,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : refl((tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3)) <=> (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3)))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(227,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[226])).
% 0.82/1.00 tff(228,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(229,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))),
% 0.82/1.00 inference(elim_unused_vars,[status(thm)],[])).
% 0.82/1.00 tff(230,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v3))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))),
% 0.82/1.00 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.82/1.00 tff(231,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v3))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))),
% 0.82/1.00 inference(transitivity,[status(thm)],[230, 229])).
% 0.82/1.00 tff(232,plain,
% 0.82/1.00 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : rewrite(((tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v3))) <=> ((~(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v3))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(233,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v3))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v3)))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[232])).
% 0.82/1.00 tff(234,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v3))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))),
% 0.82/1.00 inference(transitivity,[status(thm)],[233, 231])).
% 0.82/1.00 tff(235,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom619')).
% 0.82/1.00 tff(236,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.82/1.00 tff(237,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[236, 228])).
% 0.82/1.00 tff(238,plain,(
% 0.82/1.00 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))),
% 0.82/1.00 inference(skolemize,[status(sab)],[237])).
% 0.82/1.00 tff(239,plain,
% 0.82/1.00 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[238, 227])).
% 0.82/1.00 tff(240,plain,
% 0.82/1.00 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))) | (tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|))) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(241,plain,
% 0.82/1.00 (tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|))) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.82/1.00 tff(242,plain,
% 0.82/1.00 (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)) = tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun_A__questionmark_v1_116(|'j$'|)))),
% 0.82/1.00 inference(symmetry,[status(thm)],[241])).
% 0.82/1.00 tff(243,plain,
% 0.82/1.00 (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)) = tptp_fun__comp_j_(|'g$'|, |'id$'|)),
% 0.82/1.00 inference(transitivity,[status(thm)],[242, 225])).
% 0.82/1.00 tff(244,plain,
% 0.82/1.00 (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image_a_(tptp_fun__comp_j_(|'g$'|, |'id$'|), tptp_fun__collect_b_(|'top$d'|))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[243])).
% 0.82/1.01 tff(245,plain,
% 0.82/1.01 (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), |'top$'|)),
% 0.82/1.01 inference(transitivity,[status(thm)],[244, 133, 128, 119, 115, 111, 106, 96, 95])).
% 0.82/1.01 tff(246,plain,
% 0.82/1.01 (tptp_fun__member__(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)), tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__collect_b_(|'top$d'|))) <=> tptp_fun__member__(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)), tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), |'top$'|))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[245])).
% 0.82/1.01 tff(247,plain,
% 0.82/1.01 (tptp_fun__member__(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)), tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), |'top$'|)) <=> tptp_fun__member__(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)), tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__collect_b_(|'top$d'|)))),
% 0.82/1.01 inference(symmetry,[status(thm)],[246])).
% 0.82/1.01 tff(248,plain,
% 0.82/1.01 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun$'|] : refl(tptp_fun__member__(tptp_fun__fun_app_c_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image__(A__questionmark_v0, |'top$'|)) <=> tptp_fun__member__(tptp_fun__fun_app_c_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image__(A__questionmark_v0, |'top$'|)))),
% 0.82/1.01 inference(bind,[status(th)],[])).
% 0.82/1.01 tff(249,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun$'|] : tptp_fun__member__(tptp_fun__fun_app_c_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image__(A__questionmark_v0, |'top$'|)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun$'|] : tptp_fun__member__(tptp_fun__fun_app_c_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image__(A__questionmark_v0, |'top$'|))),
% 0.82/1.01 inference(quant_intro,[status(thm)],[248])).
% 0.82/1.01 tff(250,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun$'|] : tptp_fun__member__(tptp_fun__fun_app_c_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image__(A__questionmark_v0, |'top$'|)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun$'|] : tptp_fun__member__(tptp_fun__fun_app_c_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image__(A__questionmark_v0, |'top$'|))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(251,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun$'|] : tptp_fun__member__(tptp_fun__fun_app_c_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image__(A__questionmark_v0, |'top$'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom171')).
% 0.82/1.01 tff(252,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun$'|] : tptp_fun__member__(tptp_fun__fun_app_c_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image__(A__questionmark_v0, |'top$'|))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.82/1.01 tff(253,plain,(
% 0.82/1.01 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun$'|] : tptp_fun__member__(tptp_fun__fun_app_c_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image__(A__questionmark_v0, |'top$'|))),
% 0.82/1.01 inference(skolemize,[status(sab)],[252])).
% 0.82/1.01 tff(254,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun$'|] : tptp_fun__member__(tptp_fun__fun_app_c_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image__(A__questionmark_v0, |'top$'|))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.82/1.01 tff(255,plain,
% 0.82/1.01 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun$'|] : tptp_fun__member__(tptp_fun__fun_app_c_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image__(A__questionmark_v0, |'top$'|))) | tptp_fun__member__(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)), tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), |'top$'|))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(256,plain,
% 0.82/1.01 (tptp_fun__member__(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)), tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), |'top$'|))),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.82/1.01 tff(257,plain,
% 0.82/1.01 (tptp_fun__member__(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)), tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__collect_b_(|'top$d'|)))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[256, 247])).
% 0.82/1.01 tff(258,plain,
% 0.82/1.01 (^[A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : refl(((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)) <=> ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)))),
% 0.82/1.01 inference(bind,[status(th)],[])).
% 0.82/1.01 tff(259,plain,
% 0.82/1.01 (![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)) <=> ![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 0.82/1.01 inference(quant_intro,[status(thm)],[258])).
% 0.82/1.01 tff(260,plain,
% 0.82/1.01 (![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)) <=> ![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(261,plain,
% 0.82/1.01 (^[A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : rewrite((tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2)) => (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)) <=> ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)))),
% 0.82/1.01 inference(bind,[status(th)],[])).
% 0.82/1.01 tff(262,plain,
% 0.82/1.01 (![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : (tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2)) => (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)) <=> ![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 0.82/1.01 inference(quant_intro,[status(thm)],[261])).
% 0.82/1.01 tff(263,axiom,(![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : (tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2)) => (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom342')).
% 0.82/1.01 tff(264,plain,
% 0.82/1.01 (![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.82/1.01 tff(265,plain,
% 0.82/1.01 (![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[264, 260])).
% 0.82/1.01 tff(266,plain,(
% 0.82/1.01 ![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 0.82/1.01 inference(skolemize,[status(sab)],[265])).
% 0.82/1.01 tff(267,plain,
% 0.82/1.01 (![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[266, 259])).
% 0.82/1.01 tff(268,plain,
% 0.82/1.01 (((~![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))) | ((~tptp_fun__member__(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)), tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(tptp_fun__collect_b_(|'top$d'|), tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|))), tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))) <=> ((~![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))) | (~tptp_fun__member__(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)), tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(tptp_fun__collect_b_(|'top$d'|), tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|))), tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(269,plain,
% 0.82/1.01 ((~![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))) | ((~tptp_fun__member__(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)), tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(tptp_fun__collect_b_(|'top$d'|), tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|))), tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(270,plain,
% 0.82/1.01 ((~![A__questionmark_v0: |'C_ell2_c_ell2_cblinfun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_set$'|] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image_a_(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_b_(A__questionmark_v1, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))) | (~tptp_fun__member__(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)), tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(tptp_fun__collect_b_(|'top$d'|), tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|))), tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.82/1.01 tff(271,plain,
% 0.82/1.01 ((~tptp_fun__member__(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)), tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(tptp_fun__collect_b_(|'top$d'|), tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|))), tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[270, 267])).
% 0.82/1.01 tff(272,plain,
% 0.82/1.01 (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(tptp_fun__collect_b_(|'top$d'|), tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|))), tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[271, 257])).
% 0.82/1.01 tff(273,plain,
% 0.82/1.01 (tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) = tptp_fun__comp_n_(|'f$'|, |'id$a'|)),
% 0.82/1.01 inference(monotonicity,[status(thm)],[158])).
% 0.82/1.01 tff(274,plain,
% 0.82/1.01 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))) | (tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(275,plain,
% 0.82/1.01 (tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[274, 89])).
% 0.82/1.01 tff(276,plain,
% 0.82/1.01 (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))),
% 0.82/1.01 inference(symmetry,[status(thm)],[275])).
% 0.82/1.01 tff(277,plain,
% 0.82/1.01 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : refl(((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) <=> ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))))),
% 0.82/1.01 inference(bind,[status(th)],[])).
% 0.82/1.01 tff(278,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))),
% 0.82/1.01 inference(quant_intro,[status(thm)],[277])).
% 0.82/1.01 tff(279,plain,
% 0.82/1.01 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : trans(monotonicity(trans(monotonicity(rewrite(((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) <=> (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))))), ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) <=> (~(~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))))))), rewrite((~(~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))))) <=> ((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))), ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) <=> ((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))))), (((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> (((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)))), rewrite((((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))), (((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))))),
% 0.82/1.01 inference(bind,[status(th)],[])).
% 0.82/1.01 tff(280,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))),
% 0.82/1.01 inference(quant_intro,[status(thm)],[279])).
% 0.82/1.01 tff(281,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(282,plain,
% 0.82/1.01 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : rewrite((((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) => (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)))),
% 0.82/1.01 inference(bind,[status(th)],[])).
% 0.82/1.01 tff(283,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) => (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.01 inference(quant_intro,[status(thm)],[282])).
% 0.82/1.01 tff(284,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)) => (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom477')).
% 0.82/1.01 tff(285,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.82/1.01 tff(286,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[285, 281])).
% 0.82/1.01 tff(287,plain,(
% 0.82/1.01 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.01 inference(skolemize,[status(sab)],[286])).
% 0.82/1.01 tff(288,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[287, 280])).
% 0.82/1.01 tff(289,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[288, 278])).
% 0.82/1.01 tff(290,plain,
% 0.82/1.01 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))) | ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (tptp_fun__inv_into_b_(|'top$'|, |'j$'|) = |'i$'|))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (tptp_fun__inv_into_b_(|'top$'|, |'j$'|) = |'i$'|))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(291,plain,
% 0.82/1.01 (((tptp_fun__inv_into_b_(|'top$'|, |'j$'|) = |'i$'|) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (tptp_fun__inv_into_b_(|'top$'|, |'j$'|) = |'i$'|))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(292,plain,
% 0.82/1.01 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))) | ((tptp_fun__inv_into_b_(|'top$'|, |'j$'|) = |'i$'|) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))) | ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (tptp_fun__inv_into_b_(|'top$'|, |'j$'|) = |'i$'|)))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[291])).
% 0.82/1.01 tff(293,plain,
% 0.82/1.01 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))) | ((tptp_fun__inv_into_b_(|'top$'|, |'j$'|) = |'i$'|) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (tptp_fun__inv_into_b_(|'top$'|, |'j$'|) = |'i$'|))),
% 0.82/1.01 inference(transitivity,[status(thm)],[292, 290])).
% 0.82/1.01 tff(294,plain,
% 0.82/1.01 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))) | ((tptp_fun__inv_into_b_(|'top$'|, |'j$'|) = |'i$'|) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(295,plain,
% 0.82/1.01 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (tptp_fun__inv_into_b_(|'top$'|, |'j$'|) = |'i$'|)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.82/1.01 tff(296,plain,
% 0.82/1.01 (tptp_fun__inv_into_b_(|'top$'|, |'j$'|) = |'i$'|),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[295, 161, 158, 289])).
% 0.82/1.01 tff(297,plain,
% 0.82/1.01 (tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)) = tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|)),
% 0.82/1.01 inference(monotonicity,[status(thm)],[296])).
% 0.82/1.01 tff(298,plain,
% 0.82/1.01 (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)),
% 0.82/1.01 inference(monotonicity,[status(thm)],[297])).
% 0.82/1.01 tff(299,plain,
% 0.82/1.01 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl(((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) <=> ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)))),
% 0.82/1.01 inference(bind,[status(th)],[])).
% 0.82/1.01 tff(300,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))),
% 0.82/1.01 inference(quant_intro,[status(thm)],[299])).
% 0.82/1.01 tff(301,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(302,plain,
% 0.82/1.01 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite((tptp_fun__register_c_(A__questionmark_v0) => tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) <=> ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)))),
% 0.82/1.01 inference(bind,[status(th)],[])).
% 0.82/1.01 tff(303,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__register_c_(A__questionmark_v0) => tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))),
% 0.82/1.01 inference(quant_intro,[status(thm)],[302])).
% 0.82/1.01 tff(304,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__register_c_(A__questionmark_v0) => tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom275')).
% 0.82/1.01 tff(305,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.82/1.01 tff(306,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[305, 301])).
% 0.82/1.01 tff(307,plain,(
% 0.82/1.01 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))),
% 0.82/1.01 inference(skolemize,[status(sab)],[306])).
% 0.82/1.01 tff(308,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[307, 300])).
% 0.82/1.01 tff(309,plain,
% 0.82/1.01 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | ((~tptp_fun__register_c_(|'j$'|)) | tptp_fun__inj_on_f_(|'j$'|, |'top$'|))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | (~tptp_fun__register_c_(|'j$'|)) | tptp_fun__inj_on_f_(|'j$'|, |'top$'|))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(310,plain,
% 0.82/1.01 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | ((~tptp_fun__register_c_(|'j$'|)) | tptp_fun__inj_on_f_(|'j$'|, |'top$'|))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(311,plain,
% 0.82/1.01 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | (~tptp_fun__register_c_(|'j$'|)) | tptp_fun__inj_on_f_(|'j$'|, |'top$'|)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.82/1.01 tff(312,plain,
% 0.82/1.01 (tptp_fun__inj_on_f_(|'j$'|, |'top$'|)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[311, 308, 164])).
% 0.82/1.01 tff(313,plain,
% 0.82/1.01 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : refl(((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)) <=> ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)))),
% 0.82/1.01 inference(bind,[status(th)],[])).
% 0.82/1.01 tff(314,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.01 inference(quant_intro,[status(thm)],[313])).
% 0.82/1.01 tff(315,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(316,plain,
% 0.82/1.01 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : rewrite((tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|) => (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)) <=> ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)))),
% 0.82/1.01 inference(bind,[status(th)],[])).
% 0.82/1.01 tff(317,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|) => (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.01 inference(quant_intro,[status(thm)],[316])).
% 0.82/1.01 tff(318,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|) => (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom285')).
% 0.82/1.01 tff(319,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.82/1.01 tff(320,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[319, 315])).
% 0.82/1.01 tff(321,plain,(
% 0.82/1.01 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.01 inference(skolemize,[status(sab)],[320])).
% 0.82/1.01 tff(322,plain,
% 0.82/1.01 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[321, 314])).
% 0.82/1.01 tff(323,plain,
% 0.82/1.01 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | ((~tptp_fun__inj_on_f_(|'j$'|, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|) = |'f$'|))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | (~tptp_fun__inj_on_f_(|'j$'|, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|) = |'f$'|))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(324,plain,
% 0.82/1.01 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | ((~tptp_fun__inj_on_f_(|'j$'|, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|) = |'f$'|))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(325,plain,
% 0.82/1.01 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | (~tptp_fun__inj_on_f_(|'j$'|, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|) = |'f$'|)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.82/1.01 tff(326,plain,
% 0.82/1.01 (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|) = |'f$'|),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[325, 322, 312])).
% 0.82/1.01 tff(327,plain,
% 0.82/1.01 (|'f$'| = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|)),
% 0.82/1.01 inference(symmetry,[status(thm)],[326])).
% 0.82/1.01 tff(328,plain,
% 0.82/1.01 (|'f$'| = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))),
% 0.82/1.01 inference(transitivity,[status(thm)],[327, 298, 276, 273, 74, 91])).
% 0.82/1.01 tff(329,plain,
% 0.82/1.01 (tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[328])).
% 0.82/1.01 tff(330,plain,
% 0.82/1.01 (tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))),
% 0.82/1.01 inference(symmetry,[status(thm)],[329])).
% 0.82/1.01 tff(331,plain,
% 0.82/1.01 (tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) = tptp_fun__comp_j_(|'g$'|, |'id$'|)),
% 0.82/1.01 inference(monotonicity,[status(thm)],[161])).
% 0.82/1.01 tff(332,plain,
% 0.82/1.01 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))) | (tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(333,plain,
% 0.82/1.01 (tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[332, 239])).
% 0.82/1.01 tff(334,plain,
% 0.82/1.01 (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|) = tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))),
% 0.82/1.01 inference(symmetry,[status(thm)],[333])).
% 0.82/1.01 tff(335,plain,
% 0.82/1.01 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl(((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) <=> ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))),
% 0.82/1.01 inference(bind,[status(th)],[])).
% 0.82/1.01 tff(336,plain,
% 0.82/1.01 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))),
% 0.82/1.01 inference(quant_intro,[status(thm)],[335])).
% 0.82/1.01 tff(337,plain,
% 0.82/1.01 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : trans(monotonicity(trans(monotonicity(rewrite(((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) <=> (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))), ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) <=> (~(~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))))), rewrite((~(~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))), ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))), (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> (((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)))), rewrite((((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))), (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))),
% 0.82/1.01 inference(bind,[status(th)],[])).
% 0.82/1.01 tff(338,plain,
% 0.82/1.01 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))),
% 0.82/1.01 inference(quant_intro,[status(thm)],[337])).
% 0.82/1.01 tff(339,plain,
% 0.82/1.01 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(340,plain,
% 0.82/1.01 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite((((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) => (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(341,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) => (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[340])).
% 0.82/1.02 tff(342,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) => (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom480')).
% 0.82/1.02 tff(343,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.82/1.02 tff(344,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[343, 339])).
% 0.82/1.02 tff(345,plain,(
% 0.82/1.02 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.02 inference(skolemize,[status(sab)],[344])).
% 0.82/1.02 tff(346,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[345, 338])).
% 0.82/1.02 tff(347,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[346, 336])).
% 0.82/1.02 tff(348,plain,
% 0.82/1.02 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))) | ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (tptp_fun__inv_into_c_(|'top$a'|, |'i$'|) = |'j$'|))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (tptp_fun__inv_into_c_(|'top$a'|, |'i$'|) = |'j$'|))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(349,plain,
% 0.82/1.02 (((tptp_fun__inv_into_c_(|'top$a'|, |'i$'|) = |'j$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (tptp_fun__inv_into_c_(|'top$a'|, |'i$'|) = |'j$'|))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(350,plain,
% 0.82/1.02 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))) | ((tptp_fun__inv_into_c_(|'top$a'|, |'i$'|) = |'j$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))) | ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (tptp_fun__inv_into_c_(|'top$a'|, |'i$'|) = |'j$'|)))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[349])).
% 0.82/1.02 tff(351,plain,
% 0.82/1.02 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))) | ((tptp_fun__inv_into_c_(|'top$a'|, |'i$'|) = |'j$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (tptp_fun__inv_into_c_(|'top$a'|, |'i$'|) = |'j$'|))),
% 0.82/1.02 inference(transitivity,[status(thm)],[350, 348])).
% 0.82/1.02 tff(352,plain,
% 0.82/1.02 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))) | ((tptp_fun__inv_into_c_(|'top$a'|, |'i$'|) = |'j$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(353,plain,
% 0.82/1.02 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (tptp_fun__inv_into_c_(|'top$a'|, |'i$'|) = |'j$'|)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.82/1.02 tff(354,plain,
% 0.82/1.02 (tptp_fun__inv_into_c_(|'top$a'|, |'i$'|) = |'j$'|),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[353, 161, 158, 347])).
% 0.82/1.02 tff(355,plain,
% 0.82/1.02 (tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(|'top$a'|, |'i$'|)) = tptp_fun__comp_k_(|'g$'|, |'j$'|)),
% 0.82/1.02 inference(monotonicity,[status(thm)],[354])).
% 0.82/1.02 tff(356,plain,
% 0.82/1.02 (tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(|'top$a'|, |'i$'|))) = tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[355])).
% 0.82/1.02 tff(357,plain,
% 0.82/1.02 (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(|'top$a'|, |'i$'|))), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)),
% 0.82/1.02 inference(monotonicity,[status(thm)],[356])).
% 0.82/1.02 tff(358,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : refl(((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) <=> ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(359,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[358])).
% 0.82/1.02 tff(360,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(361,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : rewrite((tptp_fun__register_b_(A__questionmark_v0) => tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) <=> ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(362,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__register_b_(A__questionmark_v0) => tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[361])).
% 0.82/1.02 tff(363,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__register_b_(A__questionmark_v0) => tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom277')).
% 0.82/1.02 tff(364,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.82/1.02 tff(365,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[364, 360])).
% 0.82/1.02 tff(366,plain,(
% 0.82/1.02 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))),
% 0.82/1.02 inference(skolemize,[status(sab)],[365])).
% 0.82/1.02 tff(367,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[366, 359])).
% 0.82/1.02 tff(368,plain,
% 0.82/1.02 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))) | ((~tptp_fun__register_b_(|'i$'|)) | tptp_fun__inj_on_e_(|'i$'|, |'top$a'|))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))) | (~tptp_fun__register_b_(|'i$'|)) | tptp_fun__inj_on_e_(|'i$'|, |'top$a'|))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(369,plain,
% 0.82/1.02 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))) | ((~tptp_fun__register_b_(|'i$'|)) | tptp_fun__inj_on_e_(|'i$'|, |'top$a'|))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(370,plain,
% 0.82/1.02 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))) | (~tptp_fun__register_b_(|'i$'|)) | tptp_fun__inj_on_e_(|'i$'|, |'top$a'|)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.82/1.02 tff(371,plain,
% 0.82/1.02 (tptp_fun__inj_on_e_(|'i$'|, |'top$a'|)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[370, 45, 367])).
% 0.82/1.02 tff(372,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : refl(((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1)) <=> ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1)))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(373,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[372])).
% 0.82/1.02 tff(374,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(375,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : rewrite((tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|) => (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1)) <=> ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1)))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(376,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|) => (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[375])).
% 0.82/1.02 tff(377,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|) => (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom289')).
% 0.82/1.02 tff(378,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.82/1.02 tff(379,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[378, 374])).
% 0.82/1.02 tff(380,plain,(
% 0.82/1.02 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.02 inference(skolemize,[status(sab)],[379])).
% 0.82/1.02 tff(381,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[380, 373])).
% 0.82/1.02 tff(382,plain,
% 0.82/1.02 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))) | ((~tptp_fun__inj_on_e_(|'i$'|, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(|'top$a'|, |'i$'|))), |'i$'|) = |'g$'|))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))) | (~tptp_fun__inj_on_e_(|'i$'|, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(|'top$a'|, |'i$'|))), |'i$'|) = |'g$'|))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(383,plain,
% 0.82/1.02 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))) | ((~tptp_fun__inj_on_e_(|'i$'|, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(|'top$a'|, |'i$'|))), |'i$'|) = |'g$'|))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(384,plain,
% 0.82/1.02 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))) | (~tptp_fun__inj_on_e_(|'i$'|, |'top$a'|)) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(|'top$a'|, |'i$'|))), |'i$'|) = |'g$'|)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.82/1.02 tff(385,plain,
% 0.82/1.02 (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(|'top$a'|, |'i$'|))), |'i$'|) = |'g$'|),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[384, 381, 371])).
% 0.82/1.02 tff(386,plain,
% 0.82/1.02 (|'g$'| = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(|'top$a'|, |'i$'|))), |'i$'|)),
% 0.82/1.02 inference(symmetry,[status(thm)],[385])).
% 0.82/1.02 tff(387,plain,
% 0.82/1.02 (|'g$'| = tptp_fun__comp_j_(|'g$'|, |'id$'|)),
% 0.82/1.02 inference(transitivity,[status(thm)],[386, 357, 334, 331])).
% 0.82/1.02 tff(388,plain,
% 0.82/1.02 (tptp_fun__inv_into_a_(|'top$a'|, |'g$'|) = tptp_fun__inv_into_a_(|'top$a'|, tptp_fun__comp_j_(|'g$'|, |'id$'|))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[387])).
% 0.82/1.02 tff(389,plain,
% 0.82/1.02 (tptp_fun__inv_into_a_(|'top$a'|, tptp_fun__comp_j_(|'g$'|, |'id$'|)) = tptp_fun__inv_into_a_(|'top$a'|, |'g$'|)),
% 0.82/1.02 inference(symmetry,[status(thm)],[388])).
% 0.82/1.02 tff(390,plain,
% 0.82/1.02 (tptp_fun__inv_into_a_(tptp_fun__collect_b_(|'top$d'|), tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|))) = tptp_fun__inv_into_a_(|'top$a'|, tptp_fun__comp_j_(|'g$'|, |'id$'|))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[132, 243])).
% 0.82/1.02 tff(391,plain,
% 0.82/1.02 (tptp_fun__inv_into_a_(tptp_fun__collect_b_(|'top$d'|), tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|))) = tptp_fun__inv_into_a_(|'top$a'|, |'g$'|)),
% 0.82/1.02 inference(transitivity,[status(thm)],[390, 389])).
% 0.82/1.02 tff(392,plain,
% 0.82/1.02 (tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(tptp_fun__collect_b_(|'top$d'|), tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|))), tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[391, 330])).
% 0.82/1.02 tff(393,plain,
% 0.82/1.02 (tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(tptp_fun__collect_b_(|'top$d'|), tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|))), tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))),
% 0.82/1.02 inference(symmetry,[status(thm)],[392])).
% 0.82/1.02 tff(394,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl(((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|))))) <=> ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|))))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(395,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|))))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|)))))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[394])).
% 0.82/1.02 tff(396,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) <=> (~((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))))), ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) <=> (~(~((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))))))), rewrite((~(~((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))))) <=> ((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)))), ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) <=> ((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))))), rewrite((tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|)) <=> (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|))))), (((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) | (tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|))) <=> (((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|))))))), rewrite((((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|))))) <=> ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|)))))), (((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) | (tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|))) <=> ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|)))))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(397,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) | (tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|)))))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[396])).
% 0.82/1.02 tff(398,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(399,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite(((tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) => ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|))) <=> ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(400,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) => ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[399])).
% 0.82/1.02 tff(401,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) => ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom522')).
% 0.82/1.02 tff(402,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.82/1.02 tff(403,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[402, 398])).
% 0.82/1.02 tff(404,plain,(
% 0.82/1.02 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|))) | (tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|)))),
% 0.82/1.02 inference(skolemize,[status(sab)],[403])).
% 0.82/1.02 tff(405,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|)))))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[404, 397])).
% 0.82/1.02 tff(406,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|)))))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[405, 395])).
% 0.82/1.02 tff(407,plain,
% 0.82/1.02 (tptp_fun__clinear_d_(|'id$'|) <=> tptp_fun__clinear_d_(|'id$'|)),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(408,axiom,(tptp_fun__clinear_d_(|'id$'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom456')).
% 0.82/1.02 tff(409,plain,
% 0.82/1.02 (tptp_fun__clinear_d_(|'id$'|)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.82/1.02 tff(410,plain,
% 0.82/1.02 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|)))))) | ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(|'id$'|)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)))))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|)))))) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(|'id$'|)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)))))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(411,plain,
% 0.82/1.02 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|)))))) | ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(|'id$'|)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)))))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(412,plain,
% 0.82/1.02 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = |'id$'|)))))) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|) = |'top$a'|)) | (~tptp_fun__clinear_d_(|'id$'|)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|))))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.82/1.02 tff(413,plain,
% 0.82/1.02 (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)))),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[412, 409, 118, 406])).
% 0.82/1.02 tff(414,plain,
% 0.82/1.02 (((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|))) | (tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)),
% 0.82/1.02 inference(tautology,[status(thm)],[])).
% 0.82/1.02 tff(415,plain,
% 0.82/1.02 (tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[414, 413])).
% 0.82/1.02 tff(416,plain,
% 0.82/1.02 (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(|'id$'|)) = tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[161])).
% 0.82/1.02 tff(417,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl((tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1))) <=> (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(418,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[417])).
% 0.82/1.02 tff(419,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(420,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.02 inference(elim_unused_vars,[status(thm)],[])).
% 0.82/1.02 tff(421,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v2))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.02 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.82/1.02 tff(422,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v2))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[421, 420])).
% 0.82/1.02 tff(423,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite(((tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v2))) <=> ((~(tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v2))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(424,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v2))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v2)))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[423])).
% 0.82/1.02 tff(425,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v2))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[424, 422])).
% 0.82/1.02 tff(426,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom608')).
% 0.82/1.02 tff(427,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.82/1.02 tff(428,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[427, 419])).
% 0.82/1.02 tff(429,plain,(
% 0.82/1.02 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.02 inference(skolemize,[status(sab)],[428])).
% 0.82/1.02 tff(430,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[429, 418])).
% 0.82/1.02 tff(431,plain,
% 0.82/1.02 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))) | (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(|'id$'|)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(432,plain,
% 0.82/1.02 (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(|'id$'|)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)))),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[431, 430])).
% 0.82/1.02 tff(433,plain,
% 0.82/1.02 (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(|'id$'|))),
% 0.82/1.02 inference(symmetry,[status(thm)],[432])).
% 0.82/1.02 tff(434,plain,
% 0.82/1.02 (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|),
% 0.82/1.02 inference(transitivity,[status(thm)],[433, 416, 415])).
% 0.82/1.02 tff(435,plain,
% 0.82/1.02 (tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)))) = tptp_fun__comp_j_(|'g$'|, |'id$'|)),
% 0.82/1.02 inference(monotonicity,[status(thm)],[434])).
% 0.82/1.02 tff(436,plain,
% 0.82/1.02 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))) | (tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)))) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(437,plain,
% 0.82/1.02 (tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)))) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)))),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[436, 239])).
% 0.82/1.02 tff(438,plain,
% 0.82/1.02 (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))),
% 0.82/1.02 inference(symmetry,[status(thm)],[437])).
% 0.82/1.02 tff(439,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl((~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))))) <=> (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(440,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[439])).
% 0.82/1.02 tff(441,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite((~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))))) <=> (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(442,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[441])).
% 0.82/1.02 tff(443,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))),
% 0.82/1.02 inference(transitivity,[status(thm)],[442, 440])).
% 0.82/1.02 tff(444,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : trans(monotonicity(rewrite(((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (tptp_fun__register_d_(A__questionmark_v0) & tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|) & (tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|))) <=> ((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))), rewrite((tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~(tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))) <=> (tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))), ((((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (tptp_fun__register_d_(A__questionmark_v0) & tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|) & (tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|))) & (tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~(tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))) <=> (((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|))))) & (tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))))), rewrite((((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|))))) & (tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))) <=> (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))), ((((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (tptp_fun__register_d_(A__questionmark_v0) & tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|) & (tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|))) & (tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~(tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))) <=> (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(445,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (tptp_fun__register_d_(A__questionmark_v0) & tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|) & (tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|))) & (tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~(tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[444])).
% 0.82/1.02 tff(446,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite((((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (tptp_fun__register_d_(A__questionmark_v0) & (tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|) & (tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))) & (tptp_fun__iso_register_f_(A__questionmark_v0) | ((~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~(tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))) <=> (((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (tptp_fun__register_d_(A__questionmark_v0) & tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|) & (tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|))) & (tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~(tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(447,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (tptp_fun__register_d_(A__questionmark_v0) & (tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|) & (tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))) & (tptp_fun__iso_register_f_(A__questionmark_v0) | ((~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~(tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (tptp_fun__register_d_(A__questionmark_v0) & tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|) & (tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|))) & (tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~(tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[446])).
% 0.82/1.02 tff(448,plain,
% 0.82/1.02 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_f_(A__questionmark_v0) <=> (tptp_fun__register_d_(A__questionmark_v0) & ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_f_(A__questionmark_v0) <=> (tptp_fun__register_d_(A__questionmark_v0) & ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(449,plain,
% 0.82/1.02 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite((tptp_fun__iso_register_f_(A__questionmark_v0) <=> (tptp_fun__register_d_(A__questionmark_v0) & ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))) <=> (tptp_fun__iso_register_f_(A__questionmark_v0) <=> (tptp_fun__register_d_(A__questionmark_v0) & ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(450,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_f_(A__questionmark_v0) <=> (tptp_fun__register_d_(A__questionmark_v0) & ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_f_(A__questionmark_v0) <=> (tptp_fun__register_d_(A__questionmark_v0) & ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[449])).
% 0.82/1.03 tff(451,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_f_(A__questionmark_v0) <=> (tptp_fun__register_d_(A__questionmark_v0) & ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom496')).
% 0.82/1.03 tff(452,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_f_(A__questionmark_v0) <=> (tptp_fun__register_d_(A__questionmark_v0) & ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.82/1.03 tff(453,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__iso_register_f_(A__questionmark_v0) <=> (tptp_fun__register_d_(A__questionmark_v0) & ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[452, 448])).
% 0.82/1.03 tff(454,plain,(
% 0.82/1.03 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (tptp_fun__register_d_(A__questionmark_v0) & (tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|) & (tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))) & (tptp_fun__iso_register_f_(A__questionmark_v0) | ((~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~(tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))))),
% 0.82/1.03 inference(skolemize,[status(sab)],[453])).
% 0.82/1.03 tff(455,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (tptp_fun__register_d_(A__questionmark_v0) & tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|) & (tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|))) & (tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~(tptp_fun__register_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[454, 447])).
% 0.82/1.03 tff(456,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[455, 445])).
% 0.82/1.03 tff(457,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[456, 443])).
% 0.82/1.03 tff(458,plain,
% 0.82/1.03 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))) | (~((~(tptp_fun__iso_register_f_(|'id$'|) | (~tptp_fun__register_d_(|'id$'|)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(|'id$'|, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, |'id$'|) = |'id$'|))))) | (~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|))))))))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))) | (~((~(tptp_fun__iso_register_f_(|'id$'|) | (~tptp_fun__register_d_(|'id$'|)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(|'id$'|, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, |'id$'|) = |'id$'|))))) | (~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))))))))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(459,plain,
% 0.82/1.03 ((~((~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(|'id$'|) | (~tptp_fun__register_d_(|'id$'|)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(|'id$'|, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, |'id$'|) = |'id$'|))))))) <=> (~((~(tptp_fun__iso_register_f_(|'id$'|) | (~tptp_fun__register_d_(|'id$'|)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(|'id$'|, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, |'id$'|) = |'id$'|))))) | (~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|))))))))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(460,plain,
% 0.82/1.03 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))) | (~((~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(|'id$'|) | (~tptp_fun__register_d_(|'id$'|)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(|'id$'|, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, |'id$'|) = |'id$'|)))))))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))) | (~((~(tptp_fun__iso_register_f_(|'id$'|) | (~tptp_fun__register_d_(|'id$'|)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(|'id$'|, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, |'id$'|) = |'id$'|))))) | (~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))))))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[459])).
% 0.82/1.03 tff(461,plain,
% 0.82/1.03 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))) | (~((~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(|'id$'|) | (~tptp_fun__register_d_(|'id$'|)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(|'id$'|, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, |'id$'|) = |'id$'|)))))))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))) | (~((~(tptp_fun__iso_register_f_(|'id$'|) | (~tptp_fun__register_d_(|'id$'|)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(|'id$'|, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, |'id$'|) = |'id$'|))))) | (~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))))))))),
% 0.82/1.03 inference(transitivity,[status(thm)],[460, 458])).
% 0.82/1.03 tff(462,plain,
% 0.82/1.03 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))) | (~((~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(|'id$'|) | (~tptp_fun__register_d_(|'id$'|)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(|'id$'|, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, |'id$'|) = |'id$'|)))))))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(463,plain,
% 0.82/1.03 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~tptp_fun__iso_register_f_(A__questionmark_v0)) | (~((~tptp_fun__register_d_(A__questionmark_v0)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_107(A__questionmark_v0)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(A__questionmark_v0), A__questionmark_v0) = |'id$'|)))))) | (~(tptp_fun__iso_register_f_(A__questionmark_v0) | (~tptp_fun__register_d_(A__questionmark_v0)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))))) | (~((~(tptp_fun__iso_register_f_(|'id$'|) | (~tptp_fun__register_d_(|'id$'|)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(|'id$'|, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, |'id$'|) = |'id$'|))))) | (~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|))))))))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.82/1.03 tff(464,plain,
% 0.82/1.03 (~((~(tptp_fun__iso_register_f_(|'id$'|) | (~tptp_fun__register_d_(|'id$'|)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(|'id$'|, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, |'id$'|) = |'id$'|))))) | (~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))))))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[463, 457])).
% 0.82/1.03 tff(465,plain,
% 0.82/1.03 (((~(tptp_fun__iso_register_f_(|'id$'|) | (~tptp_fun__register_d_(|'id$'|)) | ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__register_d_(A__questionmark_v1)) | (~(tptp_fun__comp_l_(|'id$'|, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, |'id$'|) = |'id$'|))))) | (~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|))))))) | ((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))))),
% 0.82/1.03 inference(tautology,[status(thm)],[])).
% 0.82/1.03 tff(466,plain,
% 0.82/1.03 ((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|))))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[465, 464])).
% 0.82/1.03 tff(467,plain,
% 0.82/1.03 (tptp_fun__iso_register_f_(|'id$'|) <=> tptp_fun__iso_register_f_(|'id$'|)),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(468,axiom,(tptp_fun__iso_register_f_(|'id$'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom460')).
% 0.82/1.03 tff(469,plain,
% 0.82/1.03 (tptp_fun__iso_register_f_(|'id$'|)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.82/1.03 tff(470,plain,
% 0.82/1.03 ((~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))))) | (~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|))))),
% 0.82/1.03 inference(tautology,[status(thm)],[])).
% 0.82/1.03 tff(471,plain,
% 0.82/1.03 ((~((~tptp_fun__iso_register_f_(|'id$'|)) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))))) | (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|))))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[470, 469])).
% 0.82/1.03 tff(472,plain,
% 0.82/1.03 (~((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[471, 466])).
% 0.82/1.03 tff(473,plain,
% 0.82/1.03 (((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|))) | (tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)),
% 0.82/1.03 inference(tautology,[status(thm)],[])).
% 0.82/1.03 tff(474,plain,
% 0.82/1.03 (tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[473, 472])).
% 0.82/1.03 tff(475,plain,
% 0.82/1.03 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl(((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|))) <=> ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|))))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(476,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[475])).
% 0.82/1.03 tff(477,plain,
% 0.82/1.03 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : trans(monotonicity(trans(monotonicity(rewrite(((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) <=> (~((~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|))))), ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|))) <=> (~(~((~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|))))))), rewrite((~(~((~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|))))) <=> ((~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))), ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|))) <=> ((~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|))))), (((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)) <=> (((~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)))), rewrite((((~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)) <=> ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))), (((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)) <=> ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(478,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[477])).
% 0.82/1.03 tff(479,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(480,plain,
% 0.82/1.03 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite((((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) => (A__questionmark_v0 = A__questionmark_v2)) <=> ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(481,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) => (A__questionmark_v0 = A__questionmark_v2)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[480])).
% 0.82/1.03 tff(482,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) => (A__questionmark_v0 = A__questionmark_v2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom548')).
% 0.82/1.03 tff(483,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.82/1.03 tff(484,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[483, 479])).
% 0.82/1.03 tff(485,plain,(
% 0.82/1.03 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2))),
% 0.82/1.03 inference(skolemize,[status(sab)],[484])).
% 0.82/1.03 tff(486,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[485, 478])).
% 0.82/1.03 tff(487,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[486, 476])).
% 0.82/1.03 tff(488,plain,
% 0.82/1.03 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))) | ((~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)) | (tptp_fun_A__questionmark_v1_107(|'id$'|) = tptp_fun_A__questionmark_v1_118(|'id$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)) | (tptp_fun_A__questionmark_v1_107(|'id$'|) = tptp_fun_A__questionmark_v1_118(|'id$'|)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(489,plain,
% 0.82/1.03 (((tptp_fun_A__questionmark_v1_107(|'id$'|) = tptp_fun_A__questionmark_v1_118(|'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|))) <=> ((~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)) | (tptp_fun_A__questionmark_v1_107(|'id$'|) = tptp_fun_A__questionmark_v1_118(|'id$'|)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(490,plain,
% 0.82/1.03 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))) | ((tptp_fun_A__questionmark_v1_107(|'id$'|) = tptp_fun_A__questionmark_v1_118(|'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))) | ((~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)) | (tptp_fun_A__questionmark_v1_107(|'id$'|) = tptp_fun_A__questionmark_v1_118(|'id$'|))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[489])).
% 0.82/1.03 tff(491,plain,
% 0.82/1.03 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))) | ((tptp_fun_A__questionmark_v1_107(|'id$'|) = tptp_fun_A__questionmark_v1_118(|'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)) | (tptp_fun_A__questionmark_v1_107(|'id$'|) = tptp_fun_A__questionmark_v1_118(|'id$'|)))),
% 0.82/1.03 inference(transitivity,[status(thm)],[490, 488])).
% 0.82/1.03 tff(492,plain,
% 0.82/1.03 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))) | ((tptp_fun_A__questionmark_v1_107(|'id$'|) = tptp_fun_A__questionmark_v1_118(|'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(493,plain,
% 0.82/1.03 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v2) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)) | (tptp_fun_A__questionmark_v1_107(|'id$'|) = tptp_fun_A__questionmark_v1_118(|'id$'|))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.82/1.03 tff(494,plain,
% 0.82/1.03 (tptp_fun_A__questionmark_v1_107(|'id$'|) = tptp_fun_A__questionmark_v1_118(|'id$'|)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[493, 487, 415, 474])).
% 0.82/1.03 tff(495,plain,
% 0.82/1.03 (((~tptp_fun__register_d_(|'id$'|)) | (~tptp_fun__register_d_(tptp_fun_A__questionmark_v1_107(|'id$'|))) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|))) | (tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)),
% 0.82/1.03 inference(tautology,[status(thm)],[])).
% 0.82/1.03 tff(496,plain,
% 0.82/1.03 (tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[495, 472])).
% 0.82/1.03 tff(497,plain,
% 0.82/1.03 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl(((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) <=> ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(498,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[497])).
% 0.82/1.03 tff(499,plain,
% 0.82/1.03 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : trans(monotonicity(trans(monotonicity(rewrite(((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)) <=> (~((~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))), ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) <=> (~(~((~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))))), rewrite((~(~((~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))) <=> ((~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))), ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) <=> ((~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))))), (((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> (((~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)))), rewrite((((~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))), (((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(500,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[499])).
% 0.82/1.03 tff(501,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(502,plain,
% 0.82/1.03 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite((((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)) => (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(503,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)) => (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[502])).
% 0.82/1.03 tff(504,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)) => (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom479')).
% 0.82/1.03 tff(505,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.82/1.03 tff(506,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[505, 501])).
% 0.82/1.03 tff(507,plain,(
% 0.82/1.03 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~((tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.82/1.03 inference(skolemize,[status(sab)],[506])).
% 0.82/1.03 tff(508,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[507, 500])).
% 0.82/1.03 tff(509,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[508, 498])).
% 0.82/1.03 tff(510,plain,
% 0.82/1.03 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))) | ((~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = tptp_fun_A__questionmark_v1_107(|'id$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = tptp_fun_A__questionmark_v1_107(|'id$'|)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(511,plain,
% 0.82/1.03 (((tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = tptp_fun_A__questionmark_v1_107(|'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|))) <=> ((~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = tptp_fun_A__questionmark_v1_107(|'id$'|)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(512,plain,
% 0.82/1.03 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))) | ((tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = tptp_fun_A__questionmark_v1_107(|'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))) | ((~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = tptp_fun_A__questionmark_v1_107(|'id$'|))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[511])).
% 0.82/1.03 tff(513,plain,
% 0.82/1.03 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))) | ((tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = tptp_fun_A__questionmark_v1_107(|'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = tptp_fun_A__questionmark_v1_107(|'id$'|)))),
% 0.82/1.03 inference(transitivity,[status(thm)],[512, 510])).
% 0.82/1.03 tff(514,plain,
% 0.82/1.03 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))) | ((tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = tptp_fun_A__questionmark_v1_107(|'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(515,plain,
% 0.82/1.03 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__inv_into_g_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)) | (~(tptp_fun__comp_l_(A__questionmark_v1, A__questionmark_v0) = |'id$'|)))) | (~(tptp_fun__comp_l_(tptp_fun_A__questionmark_v1_107(|'id$'|), |'id$'|) = |'id$'|)) | (~(tptp_fun__comp_l_(|'id$'|, tptp_fun_A__questionmark_v1_107(|'id$'|)) = |'id$'|)) | (tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = tptp_fun_A__questionmark_v1_107(|'id$'|))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.82/1.03 tff(516,plain,
% 0.82/1.03 (tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = tptp_fun_A__questionmark_v1_107(|'id$'|)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[515, 509, 496, 474])).
% 0.82/1.03 tff(517,plain,
% 0.82/1.03 ((tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = |'id$'|) <=> (tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = |'id$'|)),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(518,axiom,(tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = |'id$'|), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom435')).
% 0.82/1.03 tff(519,plain,
% 0.82/1.03 (tptp_fun__inv_into_g_(|'top$a'|, |'id$'|) = |'id$'|),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.82/1.03 tff(520,plain,
% 0.82/1.03 (|'id$'| = tptp_fun__inv_into_g_(|'top$a'|, |'id$'|)),
% 0.82/1.03 inference(symmetry,[status(thm)],[519])).
% 0.82/1.03 tff(521,plain,
% 0.82/1.03 (|'id$'| = tptp_fun_A__questionmark_v1_118(|'id$'|)),
% 0.82/1.03 inference(transitivity,[status(thm)],[520, 516, 494])).
% 0.82/1.03 tff(522,plain,
% 0.82/1.03 (tptp_fun__comp_h_(|'i$'|, |'id$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[521])).
% 0.82/1.03 tff(523,plain,
% 0.82/1.03 (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__comp_h_(|'i$'|, |'id$'|)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[522])).
% 0.82/1.03 tff(524,plain,
% 0.82/1.03 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : refl((tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1))) <=> (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1))))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(525,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[524])).
% 0.82/1.03 tff(526,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(527,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.03 inference(elim_unused_vars,[status(thm)],[])).
% 0.82/1.03 tff(528,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~(tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v2))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.03 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.82/1.03 tff(529,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~(tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v2))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.03 inference(transitivity,[status(thm)],[528, 527])).
% 0.82/1.03 tff(530,plain,
% 0.82/1.03 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : rewrite(((tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v2))) <=> ((~(tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v2))))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(531,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v2))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~(tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v2)))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[530])).
% 0.82/1.03 tff(532,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v2))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.03 inference(transitivity,[status(thm)],[531, 529])).
% 0.82/1.03 tff(533,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom607')).
% 0.82/1.03 tff(534,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.82/1.03 tff(535,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[534, 526])).
% 0.82/1.03 tff(536,plain,(
% 0.82/1.03 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.03 inference(skolemize,[status(sab)],[535])).
% 0.82/1.03 tff(537,plain,
% 0.82/1.03 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[536, 525])).
% 0.82/1.04 tff(538,plain,
% 0.82/1.04 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), tptp_fun__comp_h_(A__questionmark_v0, A__questionmark_v1)))) | (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), |'id$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__comp_h_(|'i$'|, |'id$'|)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(539,plain,
% 0.82/1.04 (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), |'id$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__comp_h_(|'i$'|, |'id$'|))),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[538, 537])).
% 0.82/1.04 tff(540,plain,
% 0.82/1.04 (tptp_fun__comp_j_(|'g$'|, |'id$'|) = tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))),
% 0.82/1.04 inference(symmetry,[status(thm)],[331])).
% 0.82/1.04 tff(541,plain,
% 0.82/1.04 (tptp_fun__comp_j_(|'g$'|, |'id$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)),
% 0.82/1.04 inference(transitivity,[status(thm)],[540, 333])).
% 0.82/1.04 tff(542,plain,
% 0.82/1.04 (tptp_fun__comp_j_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'id$'|) = tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), |'id$'|)),
% 0.82/1.04 inference(monotonicity,[status(thm)],[541])).
% 0.82/1.04 tff(543,plain,
% 0.82/1.04 (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) = tptp_fun__comp_j_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'id$'|)),
% 0.82/1.04 inference(monotonicity,[status(thm)],[243, 161])).
% 0.82/1.04 tff(544,plain,
% 0.82/1.04 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v3)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v3))) | (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), |'j$'|)), |'i$'|))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(545,plain,
% 0.82/1.04 (tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), |'j$'|)), |'i$'|)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[544, 239])).
% 0.82/1.04 tff(546,plain,
% 0.82/1.04 (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), |'j$'|)), |'i$'|) = tptp_fun__comp_j_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))),
% 0.82/1.04 inference(symmetry,[status(thm)],[545])).
% 0.82/1.04 tff(547,plain,
% 0.82/1.04 (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), |'j$'|) = tptp_fun__comp_k_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'j$'|)),
% 0.82/1.04 inference(monotonicity,[status(thm)],[243])).
% 0.82/1.04 tff(548,plain,
% 0.82/1.04 (tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), |'j$'|)) = tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'j$'|))),
% 0.82/1.04 inference(monotonicity,[status(thm)],[547])).
% 0.82/1.04 tff(549,plain,
% 0.82/1.04 (tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'j$'|)) = tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), |'j$'|))),
% 0.82/1.04 inference(symmetry,[status(thm)],[548])).
% 0.82/1.04 tff(550,plain,
% 0.82/1.04 (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), |'j$'|)), |'i$'|)),
% 0.82/1.04 inference(monotonicity,[status(thm)],[549])).
% 0.82/1.04 tff(551,plain,
% 0.82/1.04 (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|))),
% 0.82/1.04 inference(transitivity,[status(thm)],[550, 546, 543, 542, 539, 523, 438, 435, 224, 241])).
% 0.82/1.04 tff(552,plain,
% 0.82/1.04 (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'j$'|)), |'i$'|), tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|)), tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(tptp_fun__collect_b_(|'top$d'|), tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun_A__questionmark_v1_116(|'j$'|))), tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))),
% 0.82/1.04 inference(monotonicity,[status(thm)],[551, 393])).
% 0.82/1.04 tff(553,plain,
% 0.82/1.04 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : refl((tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3)) <=> (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3)))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(554,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[553])).
% 0.82/1.04 tff(555,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(556,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3)) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/1.04 inference(elim_unused_vars,[status(thm)],[])).
% 0.82/1.04 tff(557,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : ((~(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(A__questionmark_v2, A__questionmark_v3))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/1.04 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.82/1.04 tff(558,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : ((~(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(A__questionmark_v2, A__questionmark_v3))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/1.04 inference(transitivity,[status(thm)],[557, 556])).
% 0.82/1.04 tff(559,plain,
% 0.82/1.04 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : rewrite(((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(A__questionmark_v2, A__questionmark_v3))) <=> ((~(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(A__questionmark_v2, A__questionmark_v3))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(560,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(A__questionmark_v2, A__questionmark_v3))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : ((~(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2)) | (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(A__questionmark_v2, A__questionmark_v3)))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[559])).
% 0.82/1.04 tff(561,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(A__questionmark_v2, A__questionmark_v3))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/1.04 inference(transitivity,[status(thm)],[560, 558])).
% 0.82/1.04 tff(562,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1) = A__questionmark_v2) => (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(A__questionmark_v2, A__questionmark_v3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom46')).
% 0.82/1.04 tff(563,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[562, 561])).
% 0.82/1.04 tff(564,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[563, 555])).
% 0.82/1.04 tff(565,plain,(
% 0.82/1.04 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/1.04 inference(skolemize,[status(sab)],[564])).
% 0.82/1.04 tff(566,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[565, 554])).
% 0.82/1.04 tff(567,plain,
% 0.82/1.04 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v3: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v3))) | (tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'j$'|), tptp_fun__fun_app_d_(|'i$'|, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'j$'|)), |'i$'|), tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(568,plain,
% 0.82/1.04 (tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'j$'|), tptp_fun__fun_app_d_(|'i$'|, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'j$'|)), |'i$'|), tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[567, 566])).
% 0.82/1.04 tff(569,plain,
% 0.82/1.04 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun$'|] : refl((tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v0) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, A__questionmark_v0))) <=> (tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v0) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, A__questionmark_v0))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(570,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v0) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, A__questionmark_v0))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v0) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, A__questionmark_v0)))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[569])).
% 0.82/1.04 tff(571,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v0) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, A__questionmark_v0))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v0) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, A__questionmark_v0)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(572,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v0) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, A__questionmark_v0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom96')).
% 0.82/1.04 tff(573,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v0) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, A__questionmark_v0)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[572, 571])).
% 0.82/1.04 tff(574,plain,(
% 0.82/1.04 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v0) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, A__questionmark_v0)))),
% 0.82/1.04 inference(skolemize,[status(sab)],[573])).
% 0.82/1.04 tff(575,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v0) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, A__questionmark_v0)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[574, 570])).
% 0.82/1.04 tff(576,plain,
% 0.82/1.04 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v0) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, A__questionmark_v0)))) | (tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(577,plain,
% 0.82/1.04 (tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[576, 575])).
% 0.82/1.04 tff(578,plain,
% 0.82/1.04 (tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))) = tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))),
% 0.82/1.04 inference(symmetry,[status(thm)],[577])).
% 0.82/1.04 tff(579,plain,
% 0.82/1.04 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl(((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|))))) <=> ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|))))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(580,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|))))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|)))))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[579])).
% 0.82/1.04 tff(581,plain,
% 0.82/1.04 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) <=> (~((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))))), ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) <=> (~(~((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))))))), rewrite((~(~((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))))) <=> ((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)))), ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) <=> ((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))))), rewrite((tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|)) <=> (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|))))), (((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | (tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|))) <=> (((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|))))))), rewrite((((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|))))) <=> ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|)))))), (((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | (tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|))) <=> ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|)))))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(582,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | (tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|)))))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[581])).
% 0.82/1.04 tff(583,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(584,plain,
% 0.82/1.04 (^[A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite(((tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) => ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) <=> ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(585,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) => ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|))) <=> ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[584])).
% 0.82/1.04 tff(586,axiom,(![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) => ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom532')).
% 0.82/1.04 tff(587,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.82/1.04 tff(588,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | ?[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = |'id$a'|)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[587, 583])).
% 0.82/1.04 tff(589,plain,(
% 0.82/1.04 ![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))) | (tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|)))),
% 0.82/1.04 inference(skolemize,[status(sab)],[588])).
% 0.82/1.04 tff(590,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|)))))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[589, 582])).
% 0.82/1.04 tff(591,plain,
% 0.82/1.04 (![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|)))))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[590, 580])).
% 0.82/1.04 tff(592,plain,
% 0.82/1.04 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|)))))) | ((~tptp_fun__inj_on_f_(|'j$'|, |'top$'|)) | (~tptp_fun__clinear_c_(|'j$'|)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(|'j$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)))))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|)))))) | (~tptp_fun__inj_on_f_(|'j$'|, |'top$'|)) | (~tptp_fun__clinear_c_(|'j$'|)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(|'j$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)))))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(593,plain,
% 0.82/1.04 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|)))))) | ((~tptp_fun__inj_on_f_(|'j$'|, |'top$'|)) | (~tptp_fun__clinear_c_(|'j$'|)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(|'j$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)))))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(594,plain,
% 0.82/1.04 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = |'id$a'|)))))) | (~tptp_fun__inj_on_f_(|'j$'|, |'top$'|)) | (~tptp_fun__clinear_c_(|'j$'|)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(|'j$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|))))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[593, 592])).
% 0.82/1.04 tff(595,plain,
% 0.82/1.04 (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(|'j$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)))),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[594, 591, 312, 202])).
% 0.82/1.04 tff(596,plain,
% 0.82/1.04 (((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(|'j$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|))) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)),
% 0.82/1.04 inference(tautology,[status(thm)],[])).
% 0.82/1.04 tff(597,plain,
% 0.82/1.04 (tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[596, 595])).
% 0.82/1.04 tff(598,plain,
% 0.82/1.04 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : refl(((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) <=> ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(599,plain,
% 0.82/1.04 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[598])).
% 0.82/1.04 tff(600,plain,
% 0.82/1.04 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : trans(monotonicity(trans(monotonicity(rewrite(((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)) <=> (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))))), ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) <=> (~(~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))))))), rewrite((~(~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))), ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))))), (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)) <=> (((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)))), rewrite((((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)) <=> ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))), (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)) <=> ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(601,plain,
% 0.82/1.04 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[600])).
% 0.82/1.04 tff(602,plain,
% 0.82/1.04 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(603,plain,
% 0.82/1.04 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : rewrite((((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)) => (A__questionmark_v0 = A__questionmark_v2)) <=> ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2)))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(604,plain,
% 0.82/1.04 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)) => (A__questionmark_v0 = A__questionmark_v2)) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2))),
% 0.88/1.04 inference(quant_intro,[status(thm)],[603])).
% 0.88/1.04 tff(605,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)) => (A__questionmark_v0 = A__questionmark_v2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom551')).
% 0.88/1.04 tff(606,plain,
% 0.88/1.04 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.88/1.04 tff(607,plain,
% 0.88/1.04 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[606, 602])).
% 0.88/1.04 tff(608,plain,(
% 0.88/1.04 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|))) | (A__questionmark_v0 = A__questionmark_v2))),
% 0.88/1.04 inference(skolemize,[status(sab)],[607])).
% 0.88/1.04 tff(609,plain,
% 0.88/1.04 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[608, 601])).
% 0.88/1.04 tff(610,plain,
% 0.88/1.04 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[609, 599])).
% 0.88/1.04 tff(611,plain,
% 0.88/1.04 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(612,plain,
% 0.88/1.04 (((tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(613,plain,
% 0.88/1.04 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | ((tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[612])).
% 0.88/1.04 tff(614,plain,
% 0.88/1.04 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | ((tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)))),
% 0.88/1.04 inference(transitivity,[status(thm)],[613, 611])).
% 0.88/1.04 tff(615,plain,
% 0.88/1.04 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | ((tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(616,plain,
% 0.88/1.04 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.88/1.04 tff(617,plain,
% 0.88/1.04 (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[616, 610, 597, 434])).
% 0.88/1.04 tff(618,plain,
% 0.88/1.04 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | ((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = |'i$'|))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = |'i$'|))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(619,plain,
% 0.88/1.04 (((tptp_fun_A__questionmark_v1_123(|'j$'|) = |'i$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|))) <=> ((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = |'i$'|))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(620,plain,
% 0.88/1.04 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | ((tptp_fun_A__questionmark_v1_123(|'j$'|) = |'i$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | ((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = |'i$'|)))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[619])).
% 0.88/1.04 tff(621,plain,
% 0.88/1.04 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | ((tptp_fun_A__questionmark_v1_123(|'j$'|) = |'i$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = |'i$'|))),
% 0.88/1.04 inference(transitivity,[status(thm)],[620, 618])).
% 0.88/1.04 tff(622,plain,
% 0.88/1.04 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | ((tptp_fun_A__questionmark_v1_123(|'j$'|) = |'i$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(623,plain,
% 0.88/1.04 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v2: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = |'id$'|)))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = |'id$a'|)) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = |'i$'|)),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[622, 621])).
% 0.88/1.04 tff(624,plain,
% 0.88/1.04 (tptp_fun_A__questionmark_v1_123(|'j$'|) = |'i$'|),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[623, 161, 610, 597])).
% 0.88/1.04 tff(625,plain,
% 0.88/1.04 (|'i$'| = tptp_fun_A__questionmark_v1_123(|'j$'|)),
% 0.88/1.04 inference(symmetry,[status(thm)],[624])).
% 0.88/1.04 tff(626,plain,
% 0.88/1.04 (|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))),
% 0.88/1.04 inference(transitivity,[status(thm)],[625, 617])).
% 0.88/1.04 tff(627,plain,
% 0.88/1.04 (tptp_fun__fun_app_d_(|'i$'|, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))) = tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[626, 578])).
% 0.88/1.04 tff(628,plain,
% 0.88/1.04 (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))) = tptp_fun__fun_app_d_(|'i$'|, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))),
% 0.88/1.04 inference(symmetry,[status(thm)],[627])).
% 0.88/1.04 tff(629,plain,
% 0.88/1.04 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite((~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))))) <=> (~((~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))))))),
% 0.88/1.04 inference(bind,[status(th)],[])).
% 0.88/1.04 tff(630,plain,
% 0.88/1.04 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))))))),
% 0.88/1.05 inference(quant_intro,[status(thm)],[629])).
% 0.88/1.05 tff(631,plain,
% 0.88/1.05 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : refl((~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))))) <=> (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))))))),
% 0.88/1.05 inference(bind,[status(th)],[])).
% 0.88/1.05 tff(632,plain,
% 0.88/1.05 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))))))),
% 0.88/1.05 inference(quant_intro,[status(thm)],[631])).
% 0.88/1.05 tff(633,plain,
% 0.88/1.05 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite((~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))))) <=> (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))))))),
% 0.88/1.05 inference(bind,[status(th)],[])).
% 0.88/1.05 tff(634,plain,
% 0.88/1.05 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))))))),
% 0.88/1.05 inference(quant_intro,[status(thm)],[633])).
% 0.88/1.05 tff(635,plain,
% 0.88/1.05 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))))))),
% 0.88/1.05 inference(transitivity,[status(thm)],[634, 632])).
% 0.88/1.05 tff(636,plain,
% 0.88/1.05 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) <=> (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))), ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) <=> (~(~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))))), rewrite((~(~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))), ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))), rewrite((![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)) <=> (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))), (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))) <=> (((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))))), rewrite((((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))), (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))))), trans(monotonicity(rewrite(((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) <=> (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))), ((((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0)))) <=> ((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))) | (~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0)))))), rewrite(((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))) | (~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0)))) <=> ((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))), ((((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0)))) <=> ((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))))), ((((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))) & (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))))) <=> (((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))) & ((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))))), rewrite((((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))) & ((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))) <=> (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))))))), ((((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))) & (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))))) <=> (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))))))))),
% 0.88/1.05 inference(bind,[status(th)],[])).
% 0.88/1.05 tff(637,plain,
% 0.88/1.05 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))) & (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))))))),
% 0.88/1.05 inference(quant_intro,[status(thm)],[636])).
% 0.88/1.05 tff(638,plain,
% 0.88/1.05 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : rewrite((((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))) & (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | ((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0)))))) <=> (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))) & (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))))))),
% 0.88/1.05 inference(bind,[status(th)],[])).
% 0.88/1.05 tff(639,plain,
% 0.88/1.05 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))) & (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | ((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0)))))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))) & (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0)))))),
% 0.88/1.05 inference(quant_intro,[status(thm)],[638])).
% 0.88/1.05 tff(640,plain,
% 0.88/1.05 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) <=> (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) <=> (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(641,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) <=> (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom556')).
% 0.88/1.05 tff(642,plain,
% 0.88/1.05 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) <=> (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[641, 640])).
% 0.88/1.05 tff(643,plain,(
% 0.88/1.05 ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))) & (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | ((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))))))),
% 0.88/1.05 inference(skolemize,[status(sab)],[642])).
% 0.88/1.05 tff(644,plain,
% 0.88/1.05 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2) & ![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))) & (((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0)))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[643, 639])).
% 0.88/1.05 tff(645,plain,
% 0.88/1.05 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[644, 637])).
% 0.88/1.05 tff(646,plain,
% 0.88/1.05 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2)))))) | (~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))))))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[645, 635])).
% 0.88/1.05 tff(647,plain,
% 0.88/1.05 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[646, 630])).
% 0.88/1.05 tff(648,plain,
% 0.88/1.05 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))))))) | (~((~((~(tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~(tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|))))))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))))))) | (~((~((~(tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~(tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(649,plain,
% 0.88/1.05 ((~((~((~(tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~(tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))))))) <=> (~((~((~(tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~(tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(650,plain,
% 0.88/1.05 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))))))) | (~((~((~(tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~(tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2))))))))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))))))) | (~((~((~(tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~(tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[649])).
% 0.88/1.05 tff(651,plain,
% 0.88/1.05 (((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))))))) | (~((~((~(tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~(tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2))))))))) <=> ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))))))) | (~((~((~(tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~(tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))))))),
% 0.88/1.05 inference(transitivity,[status(thm)],[650, 648])).
% 0.88/1.05 tff(652,plain,
% 0.88/1.05 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))))))) | (~((~((~(tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~(tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2))))))))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(653,plain,
% 0.88/1.05 ((~![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|] : (~((~((~(tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_51(A__questionmark_v1, A__questionmark_v0))) | (~(tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) = tptp_fun_A__questionmark_v2_97(A__questionmark_v1, A__questionmark_v0))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)))))) | (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(A__questionmark_v0, tptp_fun__fun_app_g_(A__questionmark_v1, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(A__questionmark_v1, tptp_fun__fun_app_d_(A__questionmark_v0, A__questionmark_v2)) = A__questionmark_v2))))))))) | (~((~((~(tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~(tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|))))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.88/1.05 tff(654,plain,
% 0.88/1.05 (~((~((~(tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~(tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[653, 647])).
% 0.88/1.06 tff(655,plain,
% 0.88/1.06 (((~((~(tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_51(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~(tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) = tptp_fun_A__questionmark_v2_97(|'j$'|, tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))))) | (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|))))) | ((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))),
% 0.88/1.06 inference(tautology,[status(thm)],[])).
% 0.88/1.06 tff(656,plain,
% 0.88/1.06 ((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[655, 654])).
% 0.88/1.06 tff(657,plain,
% 0.88/1.06 (tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = tptp_fun_A__questionmark_v1_123(|'j$'|)),
% 0.88/1.06 inference(symmetry,[status(thm)],[617])).
% 0.88/1.06 tff(658,plain,
% 0.88/1.06 (tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)) = |'i$'|),
% 0.88/1.06 inference(transitivity,[status(thm)],[657, 624])).
% 0.88/1.06 tff(659,plain,
% 0.88/1.06 (tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = tptp_fun__comp_b_(|'i$'|)),
% 0.88/1.06 inference(monotonicity,[status(thm)],[658])).
% 0.88/1.06 tff(660,plain,
% 0.88/1.06 (tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)),
% 0.88/1.06 inference(monotonicity,[status(thm)],[659])).
% 0.88/1.06 tff(661,plain,
% 0.88/1.06 (tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|),
% 0.88/1.06 inference(transitivity,[status(thm)],[660, 158])).
% 0.88/1.06 tff(662,plain,
% 0.88/1.06 ((~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|))),
% 0.88/1.06 inference(tautology,[status(thm)],[])).
% 0.88/1.06 tff(663,plain,
% 0.88/1.06 ((~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))) = |'id$'|)) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|)))) | (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|))), |'j$'|) = |'id$a'|))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[662, 434])).
% 0.88/1.06 tff(664,plain,
% 0.88/1.06 (~((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2)))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[663, 661, 656])).
% 0.88/1.06 tff(665,plain,
% 0.88/1.06 (((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (~![A__questionmark_v2: |'B_ell2_b_ell2_cblinfun$'|] : (tptp_fun__fun_app_g_(|'j$'|, tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), A__questionmark_v2)) = A__questionmark_v2))) | ![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)),
% 0.88/1.06 inference(tautology,[status(thm)],[])).
% 0.88/1.06 tff(666,plain,
% 0.88/1.06 (![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[665, 664])).
% 0.88/1.06 tff(667,plain,
% 0.88/1.06 ((~![A__questionmark_v2: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, A__questionmark_v2)) = A__questionmark_v2)) | (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))) = tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(668,plain,
% 0.88/1.06 (tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))) = tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[667, 666])).
% 0.88/1.06 tff(669,plain,
% 0.88/1.06 (tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|) = tptp_fun__fun_app_d_(tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(|'id$'|)), tptp_fun__fun_app_g_(|'j$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))),
% 0.88/1.06 inference(symmetry,[status(thm)],[668])).
% 0.88/1.06 tff(670,plain,
% 0.88/1.06 (tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|) = tptp_fun__fun_app_d_(|'i$'|, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))),
% 0.88/1.06 inference(transitivity,[status(thm)],[669, 628])).
% 0.88/1.06 tff(671,plain,
% 0.88/1.06 (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)),
% 0.88/1.06 inference(monotonicity,[status(thm)],[296])).
% 0.88/1.06 tff(672,plain,
% 0.88/1.06 (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)) = tptp_fun__comp_j_(|'g$'|, |'id$'|)),
% 0.88/1.06 inference(transitivity,[status(thm)],[671, 334, 331])).
% 0.88/1.06 tff(673,plain,
% 0.88/1.06 (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|) = tptp_fun__comp_k_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'j$'|)),
% 0.88/1.06 inference(monotonicity,[status(thm)],[672])).
% 0.88/1.06 tff(674,plain,
% 0.88/1.06 (((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | ((~tptp_fun__inj_on_f_(|'j$'|, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)))) <=> ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | (~tptp_fun__inj_on_f_(|'j$'|, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(675,plain,
% 0.88/1.06 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | ((~tptp_fun__inj_on_f_(|'j$'|, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(676,plain,
% 0.88/1.06 ((~![A__questionmark_v0: |'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'|, A__questionmark_v1: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | (~tptp_fun__inj_on_f_(|'j$'|, |'top$'|)) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.88/1.06 tff(677,plain,
% 0.88/1.06 (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[676, 322, 312])).
% 0.88/1.06 tff(678,plain,
% 0.88/1.06 (tptp_fun__comp_k_(|'g$'|, |'j$'|) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), tptp_fun__inv_into_b_(|'top$'|, |'j$'|)), |'j$'|)),
% 0.88/1.06 inference(symmetry,[status(thm)],[677])).
% 0.88/1.06 tff(679,plain,
% 0.88/1.06 (tptp_fun__comp_k_(|'g$'|, |'j$'|) = tptp_fun__comp_k_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'j$'|)),
% 0.88/1.06 inference(transitivity,[status(thm)],[678, 673])).
% 0.88/1.06 tff(680,plain,
% 0.88/1.06 (tptp_fun__fun_app_c_(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__comp_j_(|'g$'|, |'id$'|), |'j$'|), tptp_fun__fun_app_d_(|'i$'|, tptp_fun__fun_app_n_(tptp_fun__inv_into_a_(|'top$a'|, |'g$'|), tptp_fun__fun_app_c_(|'f$'|, tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[679, 670])).
% 0.88/1.06 tff(681,plain,
% 0.88/1.06 (tptp_fun__fun_app_c_(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))),
% 0.88/1.06 inference(transitivity,[status(thm)],[680, 568, 552, 272])).
% 0.88/1.06 tff(682,plain,
% 0.88/1.06 ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) <=> (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))), |'i$'|))),
% 0.88/1.06 inference(commutativity,[status(thm)],[])).
% 0.88/1.06 tff(683,plain,
% 0.88/1.06 (|'g$'| = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)),
% 0.88/1.06 inference(transitivity,[status(thm)],[386, 357])).
% 0.88/1.06 tff(684,plain,
% 0.88/1.06 (tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))) = tptp_fun__comp__(tptp_fun__comp_n_(|'f$'|, |'id$a'|))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[93])).
% 0.88/1.06 tff(685,plain,
% 0.88/1.06 (tptp_fun__comp__(tptp_fun__comp_n_(|'f$'|, |'id$a'|)) = tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)))),
% 0.88/1.06 inference(symmetry,[status(thm)],[684])).
% 0.88/1.06 tff(686,plain,
% 0.88/1.06 (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_n_(|'f$'|, |'id$a'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))), |'i$'|)),
% 0.88/1.06 inference(monotonicity,[status(thm)],[685])).
% 0.88/1.06 tff(687,plain,
% 0.88/1.06 (|'f$'| = tptp_fun__comp_n_(|'f$'|, |'id$a'|)),
% 0.88/1.06 inference(transitivity,[status(thm)],[327, 298, 276, 273])).
% 0.88/1.06 tff(688,plain,
% 0.88/1.06 (tptp_fun__comp__(|'f$'|) = tptp_fun__comp__(tptp_fun__comp_n_(|'f$'|, |'id$a'|))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[687])).
% 0.88/1.06 tff(689,plain,
% 0.88/1.06 (tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_n_(|'f$'|, |'id$a'|)), |'i$'|)),
% 0.88/1.06 inference(monotonicity,[status(thm)],[688])).
% 0.88/1.06 tff(690,plain,
% 0.88/1.06 (tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))), |'i$'|)),
% 0.88/1.06 inference(transitivity,[status(thm)],[689, 686])).
% 0.88/1.06 tff(691,plain,
% 0.88/1.06 ((tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = |'g$'|) <=> (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[690, 683])).
% 0.88/1.06 tff(692,plain,
% 0.88/1.06 ((tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = |'g$'|) <=> (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))), |'i$'|))),
% 0.88/1.06 inference(transitivity,[status(thm)],[691, 682])).
% 0.88/1.06 tff(693,plain,
% 0.88/1.06 ((~(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = |'g$'|)) <=> (~(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))), |'i$'|)))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[692])).
% 0.88/1.06 tff(694,plain,
% 0.88/1.06 ((~(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = |'g$'|)) <=> (~(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = |'g$'|))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(695,axiom,(~(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = |'g$'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture1')).
% 0.88/1.06 tff(696,plain,
% 0.88/1.06 (~(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = |'g$'|)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.88/1.06 tff(697,plain,
% 0.88/1.06 (~(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))), |'i$'|))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[696, 693])).
% 0.88/1.06 tff(698,plain,
% 0.88/1.06 (^[A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : refl(((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1), tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1)) = tptp_fun__fun_app_c_(A__questionmark_v3, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1)))))) <=> ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1), tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1)) = tptp_fun__fun_app_c_(A__questionmark_v3, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1)))))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(699,plain,
% 0.88/1.06 (![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1), tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1)) = tptp_fun__fun_app_c_(A__questionmark_v3, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1)))))) <=> ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1), tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1)) = tptp_fun__fun_app_c_(A__questionmark_v3, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1))))))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[698])).
% 0.88/1.06 tff(700,plain,
% 0.88/1.06 (![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4))))) <=> ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(701,plain,
% 0.88/1.06 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4))))) <=> ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))))),
% 0.88/1.06 inference(elim_unused_vars,[status(thm)],[])).
% 0.88/1.06 tff(702,plain,
% 0.88/1.06 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4))))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))))),
% 0.88/1.06 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.88/1.06 tff(703,plain,
% 0.88/1.06 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4))))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1))) <=> ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))))),
% 0.88/1.06 inference(transitivity,[status(thm)],[702, 701])).
% 0.88/1.06 tff(704,plain,
% 0.88/1.06 (^[A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : trans(monotonicity(rewrite(((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|)) => (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))) <=> ((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4))))), ((((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|)) => (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))) => (tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1))) <=> (((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))) => (tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1))))), rewrite((((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))) => (tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1))) <=> ((~((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4))))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)))), ((((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|)) => (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))) => (tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1))) <=> ((~((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4))))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(705,plain,
% 0.88/1.06 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|)) => (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))) => (tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1))) <=> ![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((~((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4))))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[704])).
% 0.88/1.06 tff(706,plain,
% 0.88/1.06 (![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|)) => (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))) => (tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1))) <=> ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))))),
% 0.88/1.06 inference(transitivity,[status(thm)],[705, 703])).
% 0.88/1.06 tff(707,axiom,(![A__questionmark_v0: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : (((A__questionmark_v0 = A__questionmark_v1) & ![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : (tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|)) => (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))) => (tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom263')).
% 0.88/1.06 tff(708,plain,
% 0.88/1.06 (![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[707, 706])).
% 0.88/1.06 tff(709,plain,
% 0.88/1.06 (![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~![A__questionmark_v4: |'A_ell2_a_ell2_cblinfun$'|] : ((~tptp_fun__member_a_(A__questionmark_v4, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, A__questionmark_v4) = tptp_fun__fun_app_c_(A__questionmark_v3, A__questionmark_v4)))))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[708, 700])).
% 0.88/1.06 tff(710,plain,(
% 0.88/1.06 ![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1), tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1)) = tptp_fun__fun_app_c_(A__questionmark_v3, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1))))))),
% 0.88/1.06 inference(skolemize,[status(sab)],[709])).
% 0.88/1.06 tff(711,plain,
% 0.88/1.06 (![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1), tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1)) = tptp_fun__fun_app_c_(A__questionmark_v3, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1))))))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[710, 699])).
% 0.88/1.06 tff(712,plain,
% 0.88/1.06 (((~![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1), tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1)) = tptp_fun__fun_app_c_(A__questionmark_v3, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1))))))) | ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))), |'i$'|)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|), tptp_fun__image_e_(|'i$'|, |'top$a'|))) | (tptp_fun__fun_app_c_(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))))) <=> ((~![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1), tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1)) = tptp_fun__fun_app_c_(A__questionmark_v3, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1))))))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))), |'i$'|)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|), tptp_fun__image_e_(|'i$'|, |'top$a'|))) | (tptp_fun__fun_app_c_(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(713,plain,
% 0.88/1.06 ((~![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1), tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1)) = tptp_fun__fun_app_c_(A__questionmark_v3, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1))))))) | ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))), |'i$'|)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|), tptp_fun__image_e_(|'i$'|, |'top$a'|))) | (tptp_fun__fun_app_c_(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(714,plain,
% 0.88/1.06 ((~![A__questionmark_v1: |'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'|, A__questionmark_v2: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|, A__questionmark_v3: |'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'|] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v1)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1), tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) | (tptp_fun__fun_app_c_(A__questionmark_v2, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1)) = tptp_fun__fun_app_c_(A__questionmark_v3, tptp_fun_A__questionmark_v4_73(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1))))))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))), |'i$'|)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|), tptp_fun__image_e_(|'i$'|, |'top$a'|))) | (tptp_fun__fun_app_c_(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[713, 712])).
% 0.88/1.06 tff(715,plain,
% 0.88/1.06 ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|))), |'i$'|)) | (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|), tptp_fun__image_e_(|'i$'|, |'top$a'|))) | (tptp_fun__fun_app_c_(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[714, 711])).
% 0.88/1.06 tff(716,plain,
% 0.88/1.06 (~((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|), tptp_fun__image_e_(|'i$'|, |'top$a'|))) | (tptp_fun__fun_app_c_(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[715, 697])).
% 0.88/1.06 tff(717,plain,
% 0.88/1.06 (((~tptp_fun__member_a_(tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|), tptp_fun__image_e_(|'i$'|, |'top$a'|))) | (tptp_fun__fun_app_c_(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_c_(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|))))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(718,plain,
% 0.92/1.09 (~(tptp_fun__fun_app_c_(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun_A__questionmark_v4_73(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun_A__questionmark_v1_117(|'i$'|)), tptp_fun__comp_k_(|'g$'|, |'j$'|), |'i$'|)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[717, 716])).
% 0.92/1.09 tff(719,plain,
% 0.92/1.09 ($false),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[718, 681])).
% 0.92/1.09 % SZS output end Proof
% 0.92/1.10 % E exiting
%------------------------------------------------------------------------------