%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ITP397_1 : TPTP v8.1.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n014.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 Sep 17 04:18:57 EDT 2022

% Result   : Theorem 1.13s 1.02s
% Output   : Proof 1.24s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : ITP397_1 : TPTP v8.1.0. Released v8.0.0.
% 0.06/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33  % Computer : n014.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu Sep  1 07:38:32 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.11/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33  Usage: tptp [options] [-file:]file
% 0.11/0.33    -h, -?       prints this message.
% 0.11/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.11/0.33    -m, -model   generate model.
% 0.11/0.33    -p, -proof   generate proof.
% 0.11/0.33    -c, -core    generate unsat core of named formulas.
% 0.11/0.33    -st, -statistics display statistics.
% 0.11/0.33    -t:timeout   set timeout (in second).
% 0.11/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.11/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33    -<param>:<value> configuration parameter and value.
% 0.11/0.33    -o:<output-file> file to place output in.
% 1.13/1.02  % SZS status Theorem
% 1.13/1.02  % SZS output start Proof
% 1.13/1.02  tff(tptp_fun__member___type, type, (
% 1.13/1.02     tptp_fun__member__: ( 'C_ell2_c_ell2_cblinfun$' * 'C_ell2_c_ell2_cblinfun_set$' ) > $o)).
% 1.13/1.02  tff(tptp_fun__image___type, type, (
% 1.13/1.02     tptp_fun__image__: ( 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_set$' ) > 'C_ell2_c_ell2_cblinfun_set$')).
% 1.13/1.02  tff(tptp_fun__collect_a__type, type, (
% 1.13/1.02     tptp_fun__collect_a_: 'A_ell2_a_ell2_cblinfun_bool_fun$' > 'A_ell2_a_ell2_cblinfun_set$')).
% 1.13/1.02  tff(tptp_fun__top_c__type, type, (
% 1.13/1.02     tptp_fun__top_c_: 'A_ell2_a_ell2_cblinfun_bool_fun$')).
% 1.13/1.02  tff(tptp_fun__comp_k__type, type, (
% 1.13/1.02     tptp_fun__comp_k_: ( 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__j___type, type, (
% 1.13/1.02     tptp_fun__j__: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__fun_app_a__type, type, (
% 1.13/1.02     tptp_fun__fun_app_a_: ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_b_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun_fun$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__i___type, type, (
% 1.13/1.02     tptp_fun__i__: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__comp___type, type, (
% 1.13/1.02     tptp_fun__comp__: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_b_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun_fun$')).
% 1.13/1.02  tff(tptp_fun__f___type, type, (
% 1.13/1.02     tptp_fun__f__: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__fun_app_b__type, type, (
% 1.13/1.02     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$')).
% 1.13/1.02  tff(tptp_fun_A__questionmark_v4_100_type, type, (
% 1.13/1.02     tptp_fun_A__questionmark_v4_100: ( 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_set$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun$')).
% 1.13/1.02  tff(tptp_fun__collect_b__type, type, (
% 1.13/1.02     tptp_fun__collect_b_: 'B_ell2_b_ell2_cblinfun_bool_fun$' > 'B_ell2_b_ell2_cblinfun_set$')).
% 1.13/1.02  tff(tptp_fun__top_d__type, type, (
% 1.13/1.02     tptp_fun__top_d_: 'B_ell2_b_ell2_cblinfun_bool_fun$')).
% 1.13/1.02  tff(tptp_fun__g___type, type, (
% 1.13/1.02     tptp_fun__g__: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__image_a__type, type, (
% 1.13/1.02     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$')).
% 1.13/1.02  tff(tptp_fun__comp_j__type, type, (
% 1.13/1.02     tptp_fun__comp_j_: ( 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__fun_app_f__type, type, (
% 1.13/1.02     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$')).
% 1.13/1.02  tff(tptp_fun__comp_a__type, type, (
% 1.13/1.02     tptp_fun__comp_a_: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_b_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_fun$')).
% 1.13/1.02  tff(tptp_fun__fun_app_p__type, type, (
% 1.13/1.02     tptp_fun__fun_app_p_: ( 'B_ell2_b_ell2_cblinfun_set_b_ell2_b_ell2_cblinfun_set_fun$' * 'B_ell2_b_ell2_cblinfun_set$' ) > 'B_ell2_b_ell2_cblinfun_set$')).
% 1.13/1.02  tff(tptp_fun__image_d__type, type, (
% 1.13/1.02     tptp_fun__image_d_: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_set_b_ell2_b_ell2_cblinfun_set_fun$')).
% 1.13/1.02  tff(tptp_fun__top_a__type, type, (
% 1.13/1.02     tptp_fun__top_a_: 'B_ell2_b_ell2_cblinfun_set$')).
% 1.13/1.02  tff(tptp_fun__id___type, type, (
% 1.13/1.02     tptp_fun__id__: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__top___type, type, (
% 1.13/1.02     tptp_fun__top__: 'A_ell2_a_ell2_cblinfun_set$')).
% 1.13/1.02  tff(tptp_fun__image_e__type, type, (
% 1.13/1.02     tptp_fun__image_e_: ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_set$' ) > 'A_ell2_a_ell2_cblinfun_set$')).
% 1.13/1.02  tff(tptp_fun__fun_app_i__type, type, (
% 1.13/1.02     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$')).
% 1.13/1.02  tff(tptp_fun__comp_b__type, type, (
% 1.13/1.02     tptp_fun__comp_b_: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_a_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_fun$')).
% 1.13/1.02  tff(tptp_fun__inv_into_c__type, type, (
% 1.13/1.02     tptp_fun__inv_into_c_: ( 'B_ell2_b_ell2_cblinfun_set$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__id_a__type, type, (
% 1.13/1.02     tptp_fun__id_a_: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__iso_register___type, type, (
% 1.13/1.02     tptp_fun__iso_register__: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o)).
% 1.13/1.02  tff(tptp_fun__image_f__type, type, (
% 1.13/1.02     tptp_fun__image_f_: ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_set$' ) > 'B_ell2_b_ell2_cblinfun_set$')).
% 1.13/1.02  tff(tptp_fun__inj_on_e__type, type, (
% 1.13/1.02     tptp_fun__inj_on_e_: ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_set$' ) > $o)).
% 1.13/1.02  tff(tptp_fun__register_b__type, type, (
% 1.13/1.02     tptp_fun__register_b_: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o)).
% 1.13/1.02  tff(tptp_fun__fun_app_o__type, type, (
% 1.13/1.02     tptp_fun__fun_app_o_: ( 'A_ell2_a_ell2_cblinfun_set_a_ell2_a_ell2_cblinfun_set_fun$' * 'A_ell2_a_ell2_cblinfun_set$' ) > 'A_ell2_a_ell2_cblinfun_set$')).
% 1.13/1.02  tff(tptp_fun__image_c__type, type, (
% 1.13/1.02     tptp_fun__image_c_: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_set_a_ell2_a_ell2_cblinfun_set_fun$')).
% 1.13/1.02  tff(tptp_fun__fun_app_c__type, type, (
% 1.13/1.02     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$')).
% 1.13/1.02  tff(tptp_fun__fun_app_l__type, type, (
% 1.13/1.02     tptp_fun__fun_app_l_: ( 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun$' ) > 'A_ell2_a_ell2_cblinfun$')).
% 1.13/1.02  tff(tptp_fun__inv_into___type, type, (
% 1.13/1.02     tptp_fun__inv_into__: ( 'A_ell2_a_ell2_cblinfun_set$' * 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__fun_app_d__type, type, (
% 1.13/1.02     tptp_fun__fun_app_d_: ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun$' ) > 'A_ell2_a_ell2_cblinfun$')).
% 1.13/1.02  tff(tptp_fun__comp_n__type, type, (
% 1.13/1.02     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$')).
% 1.13/1.02  tff(tptp_fun__inv_into_b__type, type, (
% 1.13/1.02     tptp_fun__inv_into_b_: ( 'A_ell2_a_ell2_cblinfun_set$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__inj_on_f__type, type, (
% 1.13/1.02     tptp_fun__inj_on_f_: ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_set$' ) > $o)).
% 1.13/1.02  tff(tptp_fun__register_c__type, type, (
% 1.13/1.02     tptp_fun__register_c_: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o)).
% 1.13/1.02  tff(tptp_fun__member_b__type, type, (
% 1.13/1.02     tptp_fun__member_b_: ( 'B_ell2_b_ell2_cblinfun$' * 'B_ell2_b_ell2_cblinfun_set$' ) > $o)).
% 1.13/1.02  tff(tptp_fun_A__questionmark_v1_123_type, type, (
% 1.13/1.02     tptp_fun_A__questionmark_v1_123: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__comp_h__type, type, (
% 1.13/1.02     tptp_fun__comp_h_: ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun_A__questionmark_v1_118_type, type, (
% 1.13/1.02     tptp_fun_A__questionmark_v1_118: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$')).
% 1.13/1.02  tff(tptp_fun__comp_l__type, type, (
% 1.13/1.02     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$')).
% 1.13/1.02  tff(tptp_fun__clinear_d__type, type, (
% 1.13/1.02     tptp_fun__clinear_d_: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o)).
% 1.13/1.02  tff(tptp_fun__clinear_b__type, type, (
% 1.13/1.02     tptp_fun__clinear_b_: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o)).
% 1.13/1.02  tff(tptp_fun__clinear_c__type, type, (
% 1.13/1.02     tptp_fun__clinear_c_: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o)).
% 1.13/1.02  tff(1,plain,
% 1.13/1.02      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : refl((tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_a_(tptp_fun__comp__(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_v2)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2)))),
% 1.13/1.02      inference(bind,[status(th)],[])).
% 1.13/1.02  tff(2,plain,
% 1.13/1.02      (![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_v2: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))),
% 1.13/1.02      inference(quant_intro,[status(thm)],[1])).
% 1.13/1.02  tff(3,plain,
% 1.13/1.02      (![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_v2: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))),
% 1.13/1.02      inference(rewrite,[status(thm)],[])).
% 1.13/1.02  tff(4,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: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom18')).
% 1.13/1.02  tff(5,plain,
% 1.13/1.02      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))),
% 1.13/1.02      inference(modus_ponens,[status(thm)],[4, 3])).
% 1.13/1.02  tff(6,plain,(
% 1.13/1.02      ![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_v2: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))),
% 1.13/1.02      inference(skolemize,[status(sab)],[5])).
% 1.13/1.02  tff(7,plain,
% 1.13/1.02      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))),
% 1.13/1.02      inference(modus_ponens,[status(thm)],[6, 2])).
% 1.13/1.02  tff(8,plain,
% 1.13/1.02      ((~![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_v2: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__comp_j_(A__questionmark_v0, tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))) | (tptp_fun__comp_j_(|'g$'|, 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$'|))),
% 1.13/1.02      inference(quant_inst,[status(thm)],[])).
% 1.13/1.02  tff(9,plain,
% 1.13/1.02      (tptp_fun__comp_j_(|'g$'|, 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$'|)),
% 1.13/1.02      inference(unit_resolution,[status(thm)],[8, 7])).
% 1.13/1.02  tff(10,plain,
% 1.13/1.02      (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|) = tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))),
% 1.13/1.02      inference(symmetry,[status(thm)],[9])).
% 1.13/1.02  tff(11,plain,
% 1.13/1.02      (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image_a_(tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|))),
% 1.13/1.02      inference(monotonicity,[status(thm)],[10])).
% 1.13/1.02  tff(12,plain,
% 1.13/1.02      (tptp_fun__image_a_(tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun__collect_b_(|'top$d'|))),
% 1.13/1.02      inference(symmetry,[status(thm)],[11])).
% 1.13/1.02  tff(13,plain,
% 1.13/1.02      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_set$'] : refl((tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2)) <=> (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2)))),
% 1.13/1.02      inference(bind,[status(th)],[])).
% 1.13/1.02  tff(14,plain,
% 1.13/1.02      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.02      inference(quant_intro,[status(thm)],[13])).
% 1.13/1.02  tff(15,plain,
% 1.13/1.02      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.02      inference(rewrite,[status(thm)],[])).
% 1.13/1.02  tff(16,axiom,(![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom223')).
% 1.13/1.02  tff(17,plain,
% 1.13/1.02      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.02      inference(modus_ponens,[status(thm)],[16, 15])).
% 1.13/1.02  tff(18,plain,(
% 1.13/1.02      ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.02      inference(skolemize,[status(sab)],[17])).
% 1.13/1.02  tff(19,plain,
% 1.13/1.02      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.02      inference(modus_ponens,[status(thm)],[18, 14])).
% 1.13/1.02  tff(20,plain,
% 1.13/1.02      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__image_a_(tptp_fun__comp_j_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))) | (tptp_fun__image_a_(|'g$'|, tptp_fun__fun_app_p_(tptp_fun__image_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|))) = tptp_fun__image_a_(tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.02      inference(quant_inst,[status(thm)],[])).
% 1.13/1.02  tff(21,plain,
% 1.13/1.02      (tptp_fun__image_a_(|'g$'|, tptp_fun__fun_app_p_(tptp_fun__image_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|))) = tptp_fun__image_a_(tptp_fun__comp_j_(|'g$'|, tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|))),
% 1.13/1.02      inference(unit_resolution,[status(thm)],[20, 19])).
% 1.13/1.02  tff(22,plain,
% 1.13/1.02      ((tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|) = |'top$a'|) <=> (tptp_fun__fun_app_p_(tptp_fun__image_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))),
% 1.13/1.02      inference(rewrite,[status(thm)],[])).
% 1.13/1.02  tff(23,plain,
% 1.13/1.02      ((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'|)),
% 1.13/1.02      inference(rewrite,[status(thm)],[])).
% 1.13/1.02  tff(24,axiom,(tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|) = |'top$a'|), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom473')).
% 1.13/1.02  tff(25,plain,
% 1.13/1.02      (tptp_fun__fun_app_p_(tptp_fun__image_d_(|'id$'|), |'top$a'|) = |'top$a'|),
% 1.13/1.02      inference(modus_ponens,[status(thm)],[24, 23])).
% 1.13/1.02  tff(26,plain,
% 1.13/1.02      (tptp_fun__fun_app_p_(tptp_fun__image_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)),
% 1.13/1.02      inference(modus_ponens,[status(thm)],[25, 22])).
% 1.13/1.02  tff(27,plain,
% 1.13/1.02      (tptp_fun__image_a_(|'g$'|, tptp_fun__fun_app_p_(tptp_fun__image_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|))) = tptp_fun__image_a_(|'g$'|, tptp_fun__collect_b_(|'top$d'|))),
% 1.13/1.02      inference(monotonicity,[status(thm)],[26])).
% 1.13/1.02  tff(28,plain,
% 1.13/1.02      (tptp_fun__image_a_(|'g$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image_a_(|'g$'|, tptp_fun__fun_app_p_(tptp_fun__image_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.02      inference(symmetry,[status(thm)],[27])).
% 1.13/1.02  tff(29,plain,
% 1.13/1.02      ((tptp_fun__image__(|'f$'|, |'top$'|) = tptp_fun__image_a_(|'g$'|, |'top$a'|)) <=> (tptp_fun__image__(|'f$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__image_a_(|'g$'|, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.02      inference(rewrite,[status(thm)],[])).
% 1.13/1.02  tff(30,plain,
% 1.13/1.02      ((tptp_fun__image__(|'f$'|, |'top$'|) = tptp_fun__image_a_(|'g$'|, |'top$a'|)) <=> (tptp_fun__image__(|'f$'|, |'top$'|) = tptp_fun__image_a_(|'g$'|, |'top$a'|))),
% 1.13/1.02      inference(rewrite,[status(thm)],[])).
% 1.13/1.02  tff(31,axiom,(tptp_fun__image__(|'f$'|, |'top$'|) = tptp_fun__image_a_(|'g$'|, |'top$a'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom97')).
% 1.13/1.02  tff(32,plain,
% 1.13/1.02      (tptp_fun__image__(|'f$'|, |'top$'|) = tptp_fun__image_a_(|'g$'|, |'top$a'|)),
% 1.13/1.02      inference(modus_ponens,[status(thm)],[31, 30])).
% 1.13/1.02  tff(33,plain,
% 1.13/1.02      (tptp_fun__image__(|'f$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__image_a_(|'g$'|, tptp_fun__collect_b_(|'top$d'|))),
% 1.13/1.02      inference(modus_ponens,[status(thm)],[32, 29])).
% 1.13/1.02  tff(34,plain,
% 1.13/1.02      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : refl(((tptp_fun__image_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) <=> ((tptp_fun__image_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(35,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((tptp_fun__image_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((tptp_fun__image_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[34])).
% 1.13/1.03  tff(36,plain,
% 1.13/1.03      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : rewrite(((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, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(37,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((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$'] : ((tptp_fun__image_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[36])).
% 1.13/1.03  tff(38,plain,
% 1.13/1.03      (![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'|))),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(39,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$a'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom517')).
% 1.13/1.03  tff(40,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((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'|))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[39, 38])).
% 1.13/1.03  tff(41,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((tptp_fun__image_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[40, 37])).
% 1.13/1.03  tff(42,plain,(
% 1.13/1.03      ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((tptp_fun__image_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(skolemize,[status(sab)],[41])).
% 1.13/1.03  tff(43,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((tptp_fun__image_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[42, 35])).
% 1.13/1.03  tff(44,plain,
% 1.13/1.03      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((tptp_fun__image_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | ((tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(quant_inst,[status(thm)],[])).
% 1.13/1.03  tff(45,plain,
% 1.13/1.03      ((tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))),
% 1.13/1.03      inference(unit_resolution,[status(thm)],[44, 43])).
% 1.13/1.03  tff(46,plain,
% 1.13/1.03      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : refl(((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) <=> ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(47,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[46])).
% 1.13/1.03  tff(48,plain,
% 1.13/1.03      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : 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_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(49,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~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$'] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[48])).
% 1.13/1.03  tff(50,plain,
% 1.13/1.03      (![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'|))),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(51,plain,
% 1.13/1.03      (^[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$a'|)))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(52,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (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$a'|))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[51])).
% 1.13/1.03  tff(53,axiom,(![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (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/sandbox2/benchmark/theBenchmark.p','axiom543')).
% 1.13/1.03  tff(54,plain,
% 1.13/1.03      (![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$a'|))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[53, 52])).
% 1.13/1.03  tff(55,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~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'|))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[54, 50])).
% 1.13/1.03  tff(56,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[55, 49])).
% 1.13/1.03  tff(57,plain,(
% 1.13/1.03      ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(skolemize,[status(sab)],[56])).
% 1.13/1.03  tff(58,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[57, 47])).
% 1.13/1.03  tff(59,plain,
% 1.13/1.03      (tptp_fun__iso_register__(|'i$'|) <=> tptp_fun__iso_register__(|'i$'|)),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(60,axiom,(tptp_fun__iso_register__(|'i$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom4')).
% 1.13/1.03  tff(61,plain,
% 1.13/1.03      (tptp_fun__iso_register__(|'i$'|)),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[60, 59])).
% 1.13/1.03  tff(62,plain,
% 1.13/1.03      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | ((~tptp_fun__iso_register__(|'i$'|)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) <=> ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (~tptp_fun__iso_register__(|'i$'|)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(63,plain,
% 1.13/1.03      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | ((~tptp_fun__iso_register__(|'i$'|)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(quant_inst,[status(thm)],[])).
% 1.13/1.03  tff(64,plain,
% 1.13/1.03      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__iso_register__(A__questionmark_v0)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (~tptp_fun__iso_register__(|'i$'|)) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[63, 62])).
% 1.13/1.03  tff(65,plain,
% 1.13/1.03      (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)),
% 1.13/1.03      inference(unit_resolution,[status(thm)],[64, 61, 58])).
% 1.13/1.03  tff(66,plain,
% 1.13/1.03      ((~((tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.03      inference(tautology,[status(thm)],[])).
% 1.13/1.03  tff(67,plain,
% 1.13/1.03      ((~((tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)) <=> (tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|))),
% 1.13/1.03      inference(unit_resolution,[status(thm)],[66, 65])).
% 1.13/1.03  tff(68,plain,
% 1.13/1.03      (tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|)),
% 1.13/1.03      inference(unit_resolution,[status(thm)],[67, 45])).
% 1.13/1.03  tff(69,plain,
% 1.13/1.03      (tptp_fun__image__(|'f$'|, tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) = tptp_fun__image__(|'f$'|, tptp_fun__collect_a_(|'top$c'|))),
% 1.13/1.03      inference(monotonicity,[status(thm)],[68])).
% 1.13/1.03  tff(70,plain,
% 1.13/1.03      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : refl((tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, tptp_fun__collect_b_(|'top$d'|)))) <=> (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, tptp_fun__collect_b_(|'top$d'|)))))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(71,plain,
% 1.13/1.03      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, tptp_fun__collect_b_(|'top$d'|)))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, tptp_fun__collect_b_(|'top$d'|))))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[70])).
% 1.13/1.03  tff(72,plain,
% 1.13/1.03      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : rewrite((tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), |'top$a'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) <=> (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, tptp_fun__collect_b_(|'top$d'|)))))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(73,plain,
% 1.13/1.03      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), |'top$a'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, tptp_fun__collect_b_(|'top$d'|))))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[72])).
% 1.13/1.03  tff(74,plain,
% 1.13/1.03      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), |'top$a'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), |'top$a'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|)))),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(75,axiom,(![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), |'top$a'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom272')).
% 1.13/1.03  tff(76,plain,
% 1.13/1.03      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), |'top$a'|) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, |'top$a'|)))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[75, 74])).
% 1.13/1.03  tff(77,plain,
% 1.13/1.03      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, tptp_fun__collect_b_(|'top$d'|))))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[76, 73])).
% 1.13/1.03  tff(78,plain,(
% 1.13/1.03      ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, tptp_fun__collect_b_(|'top$d'|))))),
% 1.13/1.03      inference(skolemize,[status(sab)],[77])).
% 1.13/1.03  tff(79,plain,
% 1.13/1.03      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, tptp_fun__collect_b_(|'top$d'|))))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[78, 71])).
% 1.13/1.03  tff(80,plain,
% 1.13/1.03      ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image__(A__questionmark_v0, tptp_fun__image_e_(A__questionmark_v1, tptp_fun__collect_b_(|'top$d'|))))) | (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image__(|'f$'|, tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))))),
% 1.13/1.03      inference(quant_inst,[status(thm)],[])).
% 1.13/1.03  tff(81,plain,
% 1.13/1.03      (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__image__(|'f$'|, tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(unit_resolution,[status(thm)],[80, 79])).
% 1.13/1.03  tff(82,plain,
% 1.13/1.03      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : refl(((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) <=> ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(83,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[82])).
% 1.13/1.03  tff(84,plain,
% 1.13/1.03      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : rewrite(((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) <=> ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(85,plain,
% 1.13/1.03      (![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$'] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[84])).
% 1.13/1.03  tff(86,plain,
% 1.13/1.03      (![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'|))),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(87,plain,
% 1.13/1.03      (^[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$a'|)))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(88,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (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$a'|))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[87])).
% 1.13/1.03  tff(89,axiom,(![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__register_b_(A__questionmark_v0) => tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom277')).
% 1.13/1.03  tff(90,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[89, 88])).
% 1.13/1.03  tff(91,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[90, 86])).
% 1.13/1.03  tff(92,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[91, 85])).
% 1.13/1.03  tff(93,plain,(
% 1.13/1.03      ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(skolemize,[status(sab)],[92])).
% 1.13/1.03  tff(94,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[93, 83])).
% 1.13/1.03  tff(95,plain,
% 1.13/1.03      (tptp_fun__register_b_(|'i$'|) <=> tptp_fun__register_b_(|'i$'|)),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(96,axiom,(tptp_fun__register_b_(|'i$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom10')).
% 1.13/1.03  tff(97,plain,
% 1.13/1.03      (tptp_fun__register_b_(|'i$'|)),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[96, 95])).
% 1.13/1.03  tff(98,plain,
% 1.13/1.03      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) | ((~tptp_fun__register_b_(|'i$'|)) | tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)))) <=> ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) | (~tptp_fun__register_b_(|'i$'|)) | tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(99,plain,
% 1.13/1.03      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) | ((~tptp_fun__register_b_(|'i$'|)) | tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(quant_inst,[status(thm)],[])).
% 1.13/1.03  tff(100,plain,
% 1.13/1.03      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~tptp_fun__register_b_(A__questionmark_v0)) | tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) | (~tptp_fun__register_b_(|'i$'|)) | tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[99, 98])).
% 1.13/1.03  tff(101,plain,
% 1.13/1.03      (tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))),
% 1.13/1.03      inference(unit_resolution,[status(thm)],[100, 97, 94])).
% 1.13/1.03  tff(102,plain,
% 1.13/1.03      ((tptp_fun__fun_app_o_(tptp_fun__image_c_(|'id$a'|), |'top$'|) = |'top$'|) <=> (tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(103,plain,
% 1.13/1.03      ((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$'|) = |'top$'|)),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(104,axiom,(tptp_fun__fun_app_o_(tptp_fun__image_c_(|'id$a'|), |'top$'|) = |'top$'|), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom472')).
% 1.13/1.03  tff(105,plain,
% 1.13/1.03      (tptp_fun__fun_app_o_(tptp_fun__image_c_(|'id$a'|), |'top$'|) = |'top$'|),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[104, 103])).
% 1.13/1.03  tff(106,plain,
% 1.13/1.03      (tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[105, 102])).
% 1.13/1.03  tff(107,plain,
% 1.13/1.03      (^[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__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)))) <=> ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)))))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(108,plain,
% 1.13/1.03      (![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__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)))) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[107])).
% 1.13/1.03  tff(109,plain,
% 1.13/1.03      (^[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_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)) & tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) <=> (~((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)))))), ((~((tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)) & tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) <=> (~(~((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)))))))), rewrite((~(~((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)))))) <=> ((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))), ((~((tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)) & tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) <=> ((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)))))), (((~((tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)) & tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|))) <=> (((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)))) | (tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|))))), rewrite((((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)))) | (tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|))) <=> ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))), (((~((tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)) & tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|))) <=> ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(110,plain,
% 1.13/1.03      (![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_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)) & tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|))) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[109])).
% 1.13/1.03  tff(111,plain,
% 1.13/1.03      (^[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_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), |'top$'|) = |'top$'|) & tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))) | (tptp_fun__image_f_(A__questionmark_v1, |'top$'|) = |'top$a'|)) <=> ((~((tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)) & tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|))))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(112,plain,
% 1.13/1.03      (![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_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), |'top$'|) = |'top$'|) & tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))) | (tptp_fun__image_f_(A__questionmark_v1, |'top$'|) = |'top$a'|)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)) & tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[111])).
% 1.13/1.03  tff(113,plain,
% 1.13/1.03      (![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_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), |'top$'|) = |'top$'|) & tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))) | (tptp_fun__image_f_(A__questionmark_v1, |'top$'|) = |'top$a'|)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), |'top$'|) = |'top$'|) & tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))) | (tptp_fun__image_f_(A__questionmark_v1, |'top$'|) = |'top$a'|))),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(114,plain,
% 1.13/1.03      (^[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_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), |'top$'|) = |'top$'|) & tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) => (tptp_fun__image_f_(A__questionmark_v1, |'top$'|) = |'top$a'|)) <=> ((~((tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), |'top$'|) = |'top$'|) & tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))) | (tptp_fun__image_f_(A__questionmark_v1, |'top$'|) = |'top$a'|)))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(115,plain,
% 1.13/1.03      (![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_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), |'top$'|) = |'top$'|) & tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) => (tptp_fun__image_f_(A__questionmark_v1, |'top$'|) = |'top$a'|)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), |'top$'|) = |'top$'|) & tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))) | (tptp_fun__image_f_(A__questionmark_v1, |'top$'|) = |'top$a'|))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[114])).
% 1.13/1.03  tff(116,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_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), |'top$'|) = |'top$'|) & tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|)) => (tptp_fun__image_f_(A__questionmark_v1, |'top$'|) = |'top$a'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom331')).
% 1.13/1.03  tff(117,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), |'top$'|) = |'top$'|) & tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))) | (tptp_fun__image_f_(A__questionmark_v1, |'top$'|) = |'top$a'|))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[116, 115])).
% 1.13/1.03  tff(118,plain,
% 1.13/1.03      (![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_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), |'top$'|) = |'top$'|) & tptp_fun__inj_on_e_(A__questionmark_v0, |'top$a'|))) | (tptp_fun__image_f_(A__questionmark_v1, |'top$'|) = |'top$a'|))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[117, 113])).
% 1.13/1.03  tff(119,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)) & tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[118, 112])).
% 1.13/1.03  tff(120,plain,(
% 1.13/1.03      ![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_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)) & tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(skolemize,[status(sab)],[119])).
% 1.13/1.03  tff(121,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[120, 110])).
% 1.13/1.03  tff(122,plain,
% 1.13/1.03      (![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__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[121, 108])).
% 1.13/1.03  tff(123,plain,
% 1.13/1.03      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))) | ((~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))) <=> ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))) | (~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(124,plain,
% 1.13/1.03      (((tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)))) <=> ((~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(125,plain,
% 1.13/1.03      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))) | ((tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))) <=> ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))) | ((~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)))))),
% 1.13/1.03      inference(monotonicity,[status(thm)],[124])).
% 1.13/1.03  tff(126,plain,
% 1.13/1.03      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))) | ((tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))) <=> ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))) | (~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))),
% 1.13/1.03      inference(transitivity,[status(thm)],[125, 123])).
% 1.13/1.03  tff(127,plain,
% 1.13/1.03      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))) | ((tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))),
% 1.13/1.03      inference(quant_inst,[status(thm)],[])).
% 1.13/1.03  tff(128,plain,
% 1.13/1.03      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__image_f_(A__questionmark_v1, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|))))) | (~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)) | (~(tptp_fun__fun_app_o_(tptp_fun__image_c_(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_a_(|'top$c'|)))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[127, 126])).
% 1.13/1.03  tff(129,plain,
% 1.13/1.03      ((~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|))),
% 1.13/1.03      inference(unit_resolution,[status(thm)],[128, 122, 106])).
% 1.13/1.03  tff(130,plain,
% 1.13/1.03      (tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__collect_b_(|'top$d'|)),
% 1.13/1.03      inference(unit_resolution,[status(thm)],[129, 101])).
% 1.13/1.03  tff(131,plain,
% 1.13/1.03      (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|))) = tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))),
% 1.13/1.03      inference(monotonicity,[status(thm)],[130])).
% 1.13/1.03  tff(132,plain,
% 1.13/1.03      (^[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_set$'] : refl((tptp_fun__image_a_(A__questionmark_v0, tptp_fun__image_f_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__image__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2)) <=> (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__image_f_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__image__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2)))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(133,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__image_f_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__image__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2)) <=> ![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_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__image_f_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__image__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[132])).
% 1.13/1.03  tff(134,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__image_f_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__image__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2)) <=> ![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_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__image_f_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__image__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(135,axiom,(![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__image_f_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__image__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom222')).
% 1.13/1.03  tff(136,plain,
% 1.13/1.03      (![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_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__image_f_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__image__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[135, 134])).
% 1.13/1.03  tff(137,plain,(
% 1.13/1.03      ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__image_f_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__image__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.03      inference(skolemize,[status(sab)],[136])).
% 1.13/1.03  tff(138,plain,
% 1.13/1.03      (![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_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__image_f_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__image__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[137, 133])).
% 1.13/1.03  tff(139,plain,
% 1.13/1.03      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : (tptp_fun__image_a_(A__questionmark_v0, tptp_fun__image_f_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__image__(tptp_fun__comp_k_(A__questionmark_v0, A__questionmark_v1), A__questionmark_v2))) | (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|))) = tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_a_(|'top$c'|)))),
% 1.13/1.03      inference(quant_inst,[status(thm)],[])).
% 1.13/1.03  tff(140,plain,
% 1.13/1.03      (tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|))) = tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_a_(|'top$c'|))),
% 1.13/1.03      inference(unit_resolution,[status(thm)],[139, 138])).
% 1.13/1.03  tff(141,plain,
% 1.13/1.03      (tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), tptp_fun__image_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)))),
% 1.13/1.03      inference(symmetry,[status(thm)],[140])).
% 1.13/1.03  tff(142,plain,
% 1.13/1.03      (tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_a_(|'top$c'|)) = tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun__collect_b_(|'top$d'|))),
% 1.13/1.03      inference(transitivity,[status(thm)],[141, 131, 81, 69, 33, 28, 21, 12])).
% 1.13/1.03  tff(143,plain,
% 1.13/1.03      (tptp_fun__member__(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)), tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_a_(|'top$c'|))) <=> tptp_fun__member__(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)), tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(monotonicity,[status(thm)],[142])).
% 1.13/1.03  tff(144,plain,
% 1.13/1.03      (tptp_fun__member__(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)), tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) <=> tptp_fun__member__(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)), tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_a_(|'top$c'|)))),
% 1.13/1.03      inference(symmetry,[status(thm)],[143])).
% 1.13/1.03  tff(145,plain,
% 1.13/1.03      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : refl(tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) <=> tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(146,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[145])).
% 1.13/1.03  tff(147,plain,
% 1.13/1.03      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : rewrite(tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, |'top$a'|)) <=> tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))))),
% 1.13/1.03      inference(bind,[status(th)],[])).
% 1.13/1.03  tff(148,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, |'top$a'|)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(quant_intro,[status(thm)],[147])).
% 1.13/1.03  tff(149,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, |'top$a'|)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, |'top$a'|))),
% 1.13/1.03      inference(rewrite,[status(thm)],[])).
% 1.13/1.03  tff(150,axiom,(![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, |'top$a'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom172')).
% 1.13/1.03  tff(151,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, |'top$a'|))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[150, 149])).
% 1.13/1.03  tff(152,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(modus_ponens,[status(thm)],[151, 148])).
% 1.13/1.03  tff(153,plain,(
% 1.13/1.03      ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.03      inference(skolemize,[status(sab)],[152])).
% 1.13/1.03  tff(154,plain,
% 1.13/1.03      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[153, 146])).
% 1.13/1.04  tff(155,plain,
% 1.13/1.04      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$'] : tptp_fun__member__(tptp_fun__fun_app_b_(A__questionmark_v0, A__questionmark_v1), tptp_fun__image_a_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|)))) | tptp_fun__member__(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)), tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.04      inference(quant_inst,[status(thm)],[])).
% 1.13/1.04  tff(156,plain,
% 1.13/1.04      (tptp_fun__member__(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)), tptp_fun__image_a_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun__collect_b_(|'top$d'|)))),
% 1.13/1.04      inference(unit_resolution,[status(thm)],[155, 154])).
% 1.13/1.04  tff(157,plain,
% 1.13/1.04      (tptp_fun__member__(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)), tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_a_(|'top$c'|)))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[156, 144])).
% 1.13/1.04  tff(158,plain,
% 1.13/1.04      (^[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$'] : refl((tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v2))) <=> (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v2))))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(159,plain,
% 1.13/1.04      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_b_(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_v2))) <=> ![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$'] : (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v2)))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[158])).
% 1.13/1.04  tff(160,plain,
% 1.13/1.04      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_b_(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_v2))) <=> ![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$'] : (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v2)))),
% 1.13/1.04      inference(rewrite,[status(thm)],[])).
% 1.13/1.04  tff(161,axiom,(![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_b_(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_v2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom5')).
% 1.13/1.04  tff(162,plain,
% 1.13/1.04      (![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$'] : (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v2)))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[161, 160])).
% 1.13/1.04  tff(163,plain,(
% 1.13/1.04      ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_b_(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_v2)))),
% 1.13/1.04      inference(skolemize,[status(sab)],[162])).
% 1.13/1.04  tff(164,plain,
% 1.13/1.04      (![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$'] : (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_c_(A__questionmark_v0, tptp_fun__fun_app_d_(A__questionmark_v1, A__questionmark_v2)))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[163, 159])).
% 1.13/1.04  tff(165,plain,
% 1.13/1.04      ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_b_(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_v2)))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_d_(|'i$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))),
% 1.13/1.04      inference(quant_inst,[status(thm)],[])).
% 1.13/1.04  tff(166,plain,
% 1.13/1.04      (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_d_(|'i$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))),
% 1.13/1.04      inference(unit_resolution,[status(thm)],[165, 164])).
% 1.13/1.04  tff(167,plain,
% 1.13/1.04      (tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_d_(|'i$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))),
% 1.13/1.04      inference(symmetry,[status(thm)],[166])).
% 1.13/1.04  tff(168,plain,
% 1.13/1.04      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : refl((tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0))) <=> (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0))))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(169,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0))) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0)))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[168])).
% 1.13/1.04  tff(170,plain,
% 1.13/1.04      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : rewrite((tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(|'top$'|, |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0))) <=> (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0))))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(171,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(|'top$'|, |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0))) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0)))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[170])).
% 1.13/1.04  tff(172,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(|'top$'|, |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0))) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(|'top$'|, |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0)))),
% 1.13/1.04      inference(rewrite,[status(thm)],[])).
% 1.13/1.04  tff(173,axiom,(![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(|'top$'|, |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom9')).
% 1.13/1.04  tff(174,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(|'top$'|, |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0)))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[173, 172])).
% 1.13/1.04  tff(175,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0)))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[174, 171])).
% 1.13/1.04  tff(176,plain,(
% 1.13/1.04      ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0)))),
% 1.13/1.04      inference(skolemize,[status(sab)],[175])).
% 1.13/1.04  tff(177,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0)))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[176, 169])).
% 1.13/1.04  tff(178,plain,
% 1.13/1.04      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__fun_app_d_(|'i$'|, A__questionmark_v0) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, A__questionmark_v0)))) | (tptp_fun__fun_app_d_(|'i$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))),
% 1.13/1.04      inference(quant_inst,[status(thm)],[])).
% 1.13/1.04  tff(179,plain,
% 1.13/1.04      (tptp_fun__fun_app_d_(|'i$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))),
% 1.13/1.04      inference(unit_resolution,[status(thm)],[178, 177])).
% 1.13/1.04  tff(180,plain,
% 1.13/1.04      (tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))) = tptp_fun__fun_app_d_(|'i$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))),
% 1.13/1.04      inference(symmetry,[status(thm)],[179])).
% 1.13/1.04  tff(181,plain,
% 1.13/1.04      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : refl(((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(182,plain,
% 1.13/1.04      (![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__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'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$'] : ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[181])).
% 1.13/1.04  tff(183,plain,
% 1.13/1.04      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : trans(monotonicity(trans(monotonicity(rewrite(((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) <=> (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))), ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> (~(~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))))), rewrite((~(~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))), ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))), (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1)) <=> (((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1)))), rewrite((((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1)) <=> ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))), (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1)) <=> ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(184,plain,
% 1.13/1.04      (![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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[183])).
% 1.13/1.04  tff(185,plain,
% 1.13/1.04      (^[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$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1)) <=> ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1)))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(186,plain,
% 1.13/1.04      (![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$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (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$'] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[185])).
% 1.13/1.04  tff(187,plain,
% 1.13/1.04      (![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$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (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))),
% 1.13/1.04      inference(rewrite,[status(thm)],[])).
% 1.13/1.04  tff(188,plain,
% 1.13/1.04      (^[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$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) => (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)))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(189,plain,
% 1.13/1.04      (![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$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|)) => (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))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[188])).
% 1.13/1.04  tff(190,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$a'|, A__questionmark_v0) = A__questionmark_v1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom480')).
% 1.13/1.04  tff(191,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[190, 189])).
% 1.13/1.04  tff(192,plain,
% 1.13/1.04      (![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$a'|) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = |'id$'|))) | (tptp_fun__inv_into_c_(|'top$a'|, A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[191, 187])).
% 1.13/1.04  tff(193,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[192, 186])).
% 1.13/1.04  tff(194,plain,(
% 1.13/1.04      ![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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(skolemize,[status(sab)],[193])).
% 1.13/1.04  tff(195,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[194, 184])).
% 1.13/1.04  tff(196,plain,
% 1.13/1.04      (![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__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[195, 182])).
% 1.13/1.04  tff(197,plain,
% 1.13/1.04      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'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$'] : ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|))),
% 1.13/1.04      inference(rewrite,[status(thm)],[])).
% 1.13/1.04  tff(198,plain,
% 1.13/1.04      (((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|) | $false | $false) <=> (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|)),
% 1.13/1.04      inference(rewrite,[status(thm)],[])).
% 1.13/1.04  tff(199,plain,
% 1.13/1.04      ((~$true) <=> $false),
% 1.13/1.04      inference(rewrite,[status(thm)],[])).
% 1.13/1.04  tff(200,plain,
% 1.13/1.04      ((tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) <=> $true),
% 1.13/1.04      inference(rewrite,[status(thm)],[])).
% 1.13/1.04  tff(201,plain,
% 1.13/1.04      ((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) <=> (~$true)),
% 1.13/1.04      inference(monotonicity,[status(thm)],[200])).
% 1.13/1.04  tff(202,plain,
% 1.13/1.04      ((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) <=> $false),
% 1.13/1.04      inference(transitivity,[status(thm)],[201, 199])).
% 1.13/1.04  tff(203,plain,
% 1.13/1.04      ((tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) <=> $true),
% 1.13/1.04      inference(rewrite,[status(thm)],[])).
% 1.13/1.04  tff(204,plain,
% 1.13/1.04      ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) <=> (~$true)),
% 1.13/1.04      inference(monotonicity,[status(thm)],[203])).
% 1.13/1.04  tff(205,plain,
% 1.13/1.04      ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) <=> $false),
% 1.13/1.04      inference(transitivity,[status(thm)],[204, 199])).
% 1.13/1.04  tff(206,plain,
% 1.13/1.04      (((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|) | $false | $false)),
% 1.13/1.04      inference(monotonicity,[status(thm)],[205, 202])).
% 1.13/1.04  tff(207,plain,
% 1.13/1.04      (((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|)),
% 1.13/1.04      inference(transitivity,[status(thm)],[206, 198])).
% 1.13/1.04  tff(208,plain,
% 1.13/1.04      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'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$'] : ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|))),
% 1.13/1.04      inference(monotonicity,[status(thm)],[207])).
% 1.13/1.04  tff(209,plain,
% 1.13/1.04      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'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$'] : ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|))),
% 1.13/1.04      inference(transitivity,[status(thm)],[208, 197])).
% 1.13/1.04  tff(210,plain,
% 1.13/1.04      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.13/1.04      inference(quant_inst,[status(thm)],[])).
% 1.13/1.04  tff(211,plain,
% 1.13/1.04      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|)),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[210, 209])).
% 1.13/1.04  tff(212,plain,
% 1.13/1.04      (tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|) = |'j$'|),
% 1.13/1.04      inference(unit_resolution,[status(thm)],[211, 196])).
% 1.13/1.04  tff(213,plain,
% 1.13/1.04      (tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__comp_k_(|'g$'|, |'j$'|)),
% 1.13/1.04      inference(monotonicity,[status(thm)],[212])).
% 1.13/1.04  tff(214,plain,
% 1.13/1.04      (tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|))) = tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|))),
% 1.13/1.04      inference(monotonicity,[status(thm)],[213])).
% 1.13/1.04  tff(215,plain,
% 1.13/1.04      (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|))), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)),
% 1.13/1.04      inference(monotonicity,[status(thm)],[214])).
% 1.13/1.04  tff(216,plain,
% 1.13/1.04      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : refl(((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1)) <=> ((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1)))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(217,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[216])).
% 1.13/1.04  tff(218,plain,
% 1.13/1.04      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1)) <=> ((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1)))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(219,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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$'] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[218])).
% 1.13/1.04  tff(220,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(rewrite,[status(thm)],[])).
% 1.13/1.04  tff(221,plain,
% 1.13/1.04      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1)))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(222,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[221])).
% 1.13/1.04  tff(223,axiom,(![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom289')).
% 1.13/1.04  tff(224,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[223, 222])).
% 1.13/1.04  tff(225,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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$a'|, A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[224, 220])).
% 1.13/1.04  tff(226,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[225, 219])).
% 1.13/1.04  tff(227,plain,(
% 1.13/1.04      ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(skolemize,[status(sab)],[226])).
% 1.13/1.04  tff(228,plain,
% 1.13/1.04      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[227, 217])).
% 1.13/1.04  tff(229,plain,
% 1.13/1.04      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))) | ((~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|))), |'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, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))) | (~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|))), |'i$'|) = |'g$'|))),
% 1.13/1.04      inference(rewrite,[status(thm)],[])).
% 1.13/1.04  tff(230,plain,
% 1.13/1.04      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_e_(A__questionmark_v0, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))) | ((~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|))), |'i$'|) = |'g$'|))),
% 1.13/1.04      inference(quant_inst,[status(thm)],[])).
% 1.13/1.04  tff(231,plain,
% 1.13/1.04      ((~![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, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v1, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), A__questionmark_v0))), A__questionmark_v0) = A__questionmark_v1))) | (~tptp_fun__inj_on_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|))), |'i$'|) = |'g$'|)),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[230, 229])).
% 1.13/1.04  tff(232,plain,
% 1.13/1.04      (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|))), |'i$'|) = |'g$'|),
% 1.13/1.04      inference(unit_resolution,[status(thm)],[231, 228, 101])).
% 1.13/1.04  tff(233,plain,
% 1.13/1.04      (|'g$'| = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, tptp_fun__inv_into_c_(tptp_fun__collect_b_(|'top$d'|), |'i$'|))), |'i$'|)),
% 1.13/1.04      inference(symmetry,[status(thm)],[232])).
% 1.13/1.04  tff(234,plain,
% 1.13/1.04      (|'g$'| = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)),
% 1.13/1.04      inference(transitivity,[status(thm)],[233, 215])).
% 1.13/1.04  tff(235,plain,
% 1.13/1.04      (tptp_fun__fun_app_b_(|'g$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))),
% 1.13/1.04      inference(monotonicity,[status(thm)],[234])).
% 1.13/1.04  tff(236,plain,
% 1.13/1.04      (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(|'g$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))),
% 1.13/1.04      inference(symmetry,[status(thm)],[235])).
% 1.13/1.04  tff(237,plain,
% 1.13/1.04      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : refl((tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__comp_k_(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_v2)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2)))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(238,plain,
% 1.13/1.04      (![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: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2)) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[237])).
% 1.13/1.04  tff(239,plain,
% 1.13/1.04      (![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: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2)) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.04      inference(rewrite,[status(thm)],[])).
% 1.13/1.04  tff(240,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: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom20')).
% 1.13/1.04  tff(241,plain,
% 1.13/1.04      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[240, 239])).
% 1.13/1.04  tff(242,plain,(
% 1.13/1.04      ![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: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.04      inference(skolemize,[status(sab)],[241])).
% 1.13/1.04  tff(243,plain,
% 1.13/1.04      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2))),
% 1.13/1.04      inference(modus_ponens,[status(thm)],[242, 238])).
% 1.13/1.04  tff(244,plain,
% 1.13/1.04      ((~![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: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_n_(A__questionmark_v0, tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v2)) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2))) | (tptp_fun__comp_n_(|'f$'|, 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$'|))),
% 1.13/1.04      inference(quant_inst,[status(thm)],[])).
% 1.13/1.04  tff(245,plain,
% 1.13/1.04      (tptp_fun__comp_n_(|'f$'|, 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$'|)),
% 1.13/1.04      inference(unit_resolution,[status(thm)],[244, 243])).
% 1.13/1.04  tff(246,plain,
% 1.13/1.04      (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))),
% 1.13/1.04      inference(symmetry,[status(thm)],[245])).
% 1.13/1.04  tff(247,plain,
% 1.13/1.04      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : refl(((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) <=> ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(248,plain,
% 1.13/1.04      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) <=> ![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__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[247])).
% 1.13/1.04  tff(249,plain,
% 1.13/1.04      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : trans(monotonicity(trans(monotonicity(rewrite(((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) <=> (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))))), ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) <=> (~(~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))))))), rewrite((~(~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))))) <=> ((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))), ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) <=> ((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))))), (((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1)) <=> (((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1)))), rewrite((((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1)) <=> ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))), (((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1)) <=> ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(250,plain,
% 1.13/1.04      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), 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_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[249])).
% 1.13/1.04  tff(251,plain,
% 1.13/1.04      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1)))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(252,plain,
% 1.13/1.04      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(quant_intro,[status(thm)],[251])).
% 1.13/1.04  tff(253,plain,
% 1.13/1.04      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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$'|, A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.04      inference(rewrite,[status(thm)],[])).
% 1.13/1.04  tff(254,plain,
% 1.13/1.04      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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$'|, A__questionmark_v0) = A__questionmark_v1)))),
% 1.13/1.04      inference(bind,[status(th)],[])).
% 1.13/1.04  tff(255,plain,
% 1.13/1.04      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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$'|, A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.05      inference(quant_intro,[status(thm)],[254])).
% 1.13/1.05  tff(256,axiom,(![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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/sandbox2/benchmark/theBenchmark.p','axiom477')).
% 1.13/1.05  tff(257,plain,
% 1.13/1.05      (![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$'|, A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[256, 255])).
% 1.13/1.05  tff(258,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[257, 253])).
% 1.13/1.05  tff(259,plain,
% 1.13/1.05      (![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) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[258, 252])).
% 1.13/1.05  tff(260,plain,(
% 1.13/1.05      ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.05      inference(skolemize,[status(sab)],[259])).
% 1.13/1.05  tff(261,plain,
% 1.13/1.05      (![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_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[260, 250])).
% 1.13/1.05  tff(262,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[261, 248])).
% 1.13/1.05  tff(263,plain,
% 1.13/1.05      (((~![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_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'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_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|))),
% 1.13/1.05      inference(rewrite,[status(thm)],[])).
% 1.13/1.05  tff(264,plain,
% 1.13/1.05      (((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|) | $false | $false) <=> (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|)),
% 1.13/1.05      inference(rewrite,[status(thm)],[])).
% 1.13/1.05  tff(265,plain,
% 1.13/1.05      (((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) <=> ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|) | $false | $false)),
% 1.13/1.05      inference(monotonicity,[status(thm)],[202, 205])).
% 1.13/1.05  tff(266,plain,
% 1.13/1.05      (((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) <=> (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|)),
% 1.13/1.05      inference(transitivity,[status(thm)],[265, 264])).
% 1.13/1.05  tff(267,plain,
% 1.13/1.05      (((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))) | ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'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$'] : ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|))),
% 1.13/1.05      inference(monotonicity,[status(thm)],[266])).
% 1.13/1.05  tff(268,plain,
% 1.13/1.05      (((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))) | ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'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$'] : ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|))),
% 1.13/1.05      inference(transitivity,[status(thm)],[267, 263])).
% 1.13/1.05  tff(269,plain,
% 1.13/1.05      ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))) | ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))),
% 1.13/1.05      inference(quant_inst,[status(thm)],[])).
% 1.13/1.05  tff(270,plain,
% 1.13/1.05      ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ((tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))) | (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|)),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[269, 268])).
% 1.13/1.05  tff(271,plain,
% 1.13/1.05      (tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|) = |'i$'|),
% 1.13/1.05      inference(unit_resolution,[status(thm)],[270, 262])).
% 1.13/1.05  tff(272,plain,
% 1.13/1.05      (tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|)) = tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|)),
% 1.13/1.05      inference(monotonicity,[status(thm)],[271])).
% 1.13/1.05  tff(273,plain,
% 1.13/1.05      (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|)), |'j$'|) = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)),
% 1.13/1.05      inference(monotonicity,[status(thm)],[272])).
% 1.13/1.05  tff(274,plain,
% 1.13/1.05      (tptp_fun__register_c_(|'j$'|) <=> tptp_fun__register_c_(|'j$'|)),
% 1.13/1.05      inference(rewrite,[status(thm)],[])).
% 1.13/1.05  tff(275,axiom,(tptp_fun__register_c_(|'j$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom335')).
% 1.13/1.05  tff(276,plain,
% 1.13/1.05      (tptp_fun__register_c_(|'j$'|)),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[275, 274])).
% 1.13/1.05  tff(277,plain,
% 1.13/1.05      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : refl(((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) <=> ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))))),
% 1.13/1.05      inference(bind,[status(th)],[])).
% 1.13/1.05  tff(278,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))),
% 1.13/1.05      inference(quant_intro,[status(thm)],[277])).
% 1.13/1.05  tff(279,plain,
% 1.13/1.05      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : rewrite(((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|)) <=> ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))))),
% 1.13/1.05      inference(bind,[status(th)],[])).
% 1.13/1.05  tff(280,plain,
% 1.13/1.05      (![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$'] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))),
% 1.13/1.05      inference(quant_intro,[status(thm)],[279])).
% 1.13/1.05  tff(281,plain,
% 1.13/1.05      (![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$'] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))),
% 1.13/1.05      inference(rewrite,[status(thm)],[])).
% 1.13/1.05  tff(282,plain,
% 1.13/1.05      (^[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$'|)))),
% 1.13/1.05      inference(bind,[status(th)],[])).
% 1.13/1.05  tff(283,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (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$'|))),
% 1.13/1.05      inference(quant_intro,[status(thm)],[282])).
% 1.13/1.05  tff(284,axiom,(![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__register_c_(A__questionmark_v0) => tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom275')).
% 1.13/1.05  tff(285,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[284, 283])).
% 1.13/1.05  tff(286,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, |'top$'|))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[285, 281])).
% 1.13/1.05  tff(287,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[286, 280])).
% 1.13/1.05  tff(288,plain,(
% 1.13/1.05      ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))),
% 1.13/1.05      inference(skolemize,[status(sab)],[287])).
% 1.13/1.05  tff(289,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[288, 278])).
% 1.13/1.05  tff(290,plain,
% 1.13/1.05      (((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) | ((~tptp_fun__register_c_(|'j$'|)) | tptp_fun__inj_on_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)))) <=> ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) | (~tptp_fun__register_c_(|'j$'|)) | tptp_fun__inj_on_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)))),
% 1.13/1.05      inference(rewrite,[status(thm)],[])).
% 1.13/1.05  tff(291,plain,
% 1.13/1.05      ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) | ((~tptp_fun__register_c_(|'j$'|)) | tptp_fun__inj_on_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|)))),
% 1.13/1.05      inference(quant_inst,[status(thm)],[])).
% 1.13/1.05  tff(292,plain,
% 1.13/1.05      ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__register_c_(A__questionmark_v0)) | tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) | (~tptp_fun__register_c_(|'j$'|)) | tptp_fun__inj_on_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[291, 290])).
% 1.13/1.05  tff(293,plain,
% 1.13/1.05      (tptp_fun__inj_on_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|))),
% 1.13/1.05      inference(unit_resolution,[status(thm)],[292, 289, 276])).
% 1.13/1.05  tff(294,plain,
% 1.13/1.05      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : refl(((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)) <=> ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)))),
% 1.13/1.05      inference(bind,[status(th)],[])).
% 1.13/1.05  tff(295,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.05      inference(quant_intro,[status(thm)],[294])).
% 1.13/1.05  tff(296,plain,
% 1.13/1.05      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)) <=> ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)))),
% 1.13/1.05      inference(bind,[status(th)],[])).
% 1.13/1.05  tff(297,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.05      inference(quant_intro,[status(thm)],[296])).
% 1.13/1.05  tff(298,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.05      inference(rewrite,[status(thm)],[])).
% 1.13/1.05  tff(299,plain,
% 1.13/1.05      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)))),
% 1.13/1.05      inference(bind,[status(th)],[])).
% 1.13/1.05  tff(300,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.05      inference(quant_intro,[status(thm)],[299])).
% 1.13/1.05  tff(301,axiom,(![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom285')).
% 1.13/1.05  tff(302,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[301, 300])).
% 1.13/1.05  tff(303,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', 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$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[302, 298])).
% 1.13/1.05  tff(304,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[303, 297])).
% 1.13/1.05  tff(305,plain,(
% 1.13/1.05      ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.05      inference(skolemize,[status(sab)],[304])).
% 1.13/1.05  tff(306,plain,
% 1.13/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[305, 295])).
% 1.13/1.05  tff(307,plain,
% 1.13/1.05      (((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | ((~tptp_fun__inj_on_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|)), |'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, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | (~tptp_fun__inj_on_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|)), |'j$'|) = |'f$'|))),
% 1.13/1.05      inference(rewrite,[status(thm)],[])).
% 1.13/1.05  tff(308,plain,
% 1.13/1.05      ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | ((~tptp_fun__inj_on_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|)), |'j$'|) = |'f$'|))),
% 1.13/1.05      inference(quant_inst,[status(thm)],[])).
% 1.13/1.05  tff(309,plain,
% 1.13/1.05      ((~![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, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v1), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | (~tptp_fun__inj_on_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|)), |'j$'|) = |'f$'|)),
% 1.13/1.05      inference(modus_ponens,[status(thm)],[308, 307])).
% 1.13/1.05  tff(310,plain,
% 1.13/1.05      (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|)), |'j$'|) = |'f$'|),
% 1.13/1.05      inference(unit_resolution,[status(thm)],[309, 306, 293])).
% 1.13/1.05  tff(311,plain,
% 1.13/1.05      (|'f$'| = tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), tptp_fun__inv_into_b_(tptp_fun__collect_a_(|'top$c'|), |'j$'|)), |'j$'|)),
% 1.13/1.05      inference(symmetry,[status(thm)],[310])).
% 1.13/1.05  tff(312,plain,
% 1.13/1.05      (|'f$'| = tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))),
% 1.13/1.05      inference(transitivity,[status(thm)],[311, 273, 246])).
% 1.13/1.05  tff(313,plain,
% 1.13/1.05      (tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|) = tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.05      inference(monotonicity,[status(thm)],[312])).
% 1.13/1.05  tff(314,plain,
% 1.13/1.05      (tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) = tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|)),
% 1.13/1.05      inference(symmetry,[status(thm)],[313])).
% 1.13/1.05  tff(315,plain,
% 1.13/1.05      (tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)) = tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.13/1.05      inference(monotonicity,[status(thm)],[246])).
% 1.13/1.05  tff(316,plain,
% 1.13/1.05      (tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)) = tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|)),
% 1.13/1.05      inference(transitivity,[status(thm)],[315, 314])).
% 1.13/1.05  tff(317,plain,
% 1.13/1.05      (tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))) = tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), |'f$'|), tptp_fun__fun_app_b_(|'g$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))),
% 1.13/1.05      inference(monotonicity,[status(thm)],[316, 236])).
% 1.13/1.05  tff(318,plain,
% 1.13/1.05      (tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))) = tptp_fun__fun_app_d_(|'i$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))),
% 1.13/1.05      inference(transitivity,[status(thm)],[317, 180])).
% 1.13/1.05  tff(319,plain,
% 1.13/1.05      (tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))) = tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_d_(|'i$'|, tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))),
% 1.13/1.05      inference(monotonicity,[status(thm)],[318])).
% 1.13/1.05  tff(320,plain,
% 1.13/1.05      (tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))),
% 1.13/1.05      inference(transitivity,[status(thm)],[319, 167])).
% 1.13/1.05  tff(321,plain,
% 1.13/1.05      ((tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))) <=> (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))),
% 1.13/1.05      inference(monotonicity,[status(thm)],[320])).
% 1.13/1.05  tff(322,plain,
% 1.13/1.05      ((tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))) <=> (tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))),
% 1.13/1.05      inference(symmetry,[status(thm)],[321])).
% 1.13/1.05  tff(323,plain,
% 1.13/1.05      ((~(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))) <=> (~(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))),
% 1.13/1.05      inference(monotonicity,[status(thm)],[322])).
% 1.13/1.05  tff(324,plain,
% 1.13/1.05      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : refl(((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~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)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))) <=> ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~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)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))))),
% 1.13/1.05      inference(bind,[status(th)],[])).
% 1.13/1.05  tff(325,plain,
% 1.13/1.05      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~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)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))),
% 1.13/1.05      inference(quant_intro,[status(thm)],[324])).
% 1.13/1.05  tff(326,plain,
% 1.13/1.05      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) <=> (~((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))))), ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))) <=> (~(~((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))))))), rewrite((~(~((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))))) <=> ((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))))), ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))) <=> ((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))))), rewrite((tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) <=> (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))), (((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> (((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))))), rewrite((((~tptp_fun__clinear_d_(A__questionmark_v0)) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))) <=> ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))), (((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))))),
% 1.22/1.05      inference(bind,[status(th)],[])).
% 1.22/1.05  tff(327,plain,
% 1.22/1.05      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))) | (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)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))),
% 1.22/1.05      inference(quant_intro,[status(thm)],[326])).
% 1.22/1.05  tff(328,plain,
% 1.22/1.05      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : 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), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))) | ?[A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))),
% 1.22/1.05      inference(bind,[status(th)],[])).
% 1.22/1.05  tff(329,plain,
% 1.22/1.05      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(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$'] : ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))) | ?[A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.05      inference(quant_intro,[status(thm)],[328])).
% 1.22/1.05  tff(330,plain,
% 1.22/1.05      (![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$'] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))),
% 1.22/1.05      inference(rewrite,[status(thm)],[])).
% 1.22/1.05  tff(331,plain,
% 1.22/1.05      (^[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$'|))))),
% 1.22/1.05      inference(bind,[status(th)],[])).
% 1.22/1.05  tff(332,plain,
% 1.22/1.05      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((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$'|)))),
% 1.22/1.05      inference(quant_intro,[status(thm)],[331])).
% 1.22/1.05  tff(333,axiom,(![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((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/sandbox2/benchmark/theBenchmark.p','axiom522')).
% 1.22/1.05  tff(334,plain,
% 1.22/1.05      (![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$'|)))),
% 1.22/1.05      inference(modus_ponens,[status(thm)],[333, 332])).
% 1.22/1.05  tff(335,plain,
% 1.22/1.05      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(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$'] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = |'id$'|)))),
% 1.22/1.05      inference(modus_ponens,[status(thm)],[334, 330])).
% 1.22/1.05  tff(336,plain,
% 1.22/1.05      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))) | ?[A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__clinear_d_(A__questionmark_v1) & (tptp_fun__comp_l_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.05      inference(modus_ponens,[status(thm)],[335, 329])).
% 1.22/1.05  tff(337,plain,(
% 1.22/1.05      ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__clinear_d_(A__questionmark_v0) & (tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|)))) | (tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) & (tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.05      inference(skolemize,[status(sab)],[336])).
% 1.22/1.05  tff(338,plain,
% 1.22/1.05      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~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)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))),
% 1.22/1.05      inference(modus_ponens,[status(thm)],[337, 327])).
% 1.22/1.05  tff(339,plain,
% 1.22/1.05      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))),
% 1.22/1.05      inference(modus_ponens,[status(thm)],[338, 325])).
% 1.22/1.05  tff(340,plain,
% 1.22/1.05      (tptp_fun__clinear_d_(|'id$'|) <=> tptp_fun__clinear_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))),
% 1.22/1.05      inference(rewrite,[status(thm)],[])).
% 1.22/1.05  tff(341,plain,
% 1.22/1.05      (tptp_fun__clinear_d_(|'id$'|) <=> tptp_fun__clinear_d_(|'id$'|)),
% 1.22/1.05      inference(rewrite,[status(thm)],[])).
% 1.22/1.05  tff(342,axiom,(tptp_fun__clinear_d_(|'id$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom456')).
% 1.22/1.05  tff(343,plain,
% 1.22/1.05      (tptp_fun__clinear_d_(|'id$'|)),
% 1.22/1.05      inference(modus_ponens,[status(thm)],[342, 341])).
% 1.22/1.05  tff(344,plain,
% 1.22/1.05      (tptp_fun__clinear_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))),
% 1.22/1.05      inference(modus_ponens,[status(thm)],[343, 340])).
% 1.22/1.05  tff(345,plain,
% 1.22/1.05      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))) | ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~tptp_fun__clinear_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))) <=> ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~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)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~tptp_fun__clinear_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))),
% 1.22/1.05      inference(rewrite,[status(thm)],[])).
% 1.22/1.05  tff(346,plain,
% 1.22/1.05      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~tptp_fun__clinear_d_(A__questionmark_v0)) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(A__questionmark_v0))) | (~(tptp_fun__comp_l_(A__questionmark_v0, tptp_fun_A__questionmark_v1_118(A__questionmark_v0)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))) | ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~tptp_fun__clinear_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))),
% 1.22/1.05      inference(quant_inst,[status(thm)],[])).
% 1.22/1.05  tff(347,plain,
% 1.22/1.05      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__fun_app_p_(tptp_fun__image_d_(A__questionmark_v0), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~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)) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))) | (~(tptp_fun__fun_app_p_(tptp_fun__image_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)), tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_b_(|'top$d'|))) | (~tptp_fun__clinear_d_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))),
% 1.22/1.05      inference(modus_ponens,[status(thm)],[346, 345])).
% 1.22/1.05  tff(348,plain,
% 1.22/1.05      (~((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.05      inference(unit_resolution,[status(thm)],[347, 344, 26, 339])).
% 1.22/1.05  tff(349,plain,
% 1.22/1.05      (((~tptp_fun__clinear_d_(tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))),
% 1.22/1.05      inference(tautology,[status(thm)],[])).
% 1.22/1.05  tff(350,plain,
% 1.22/1.05      (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)),
% 1.22/1.05      inference(unit_resolution,[status(thm)],[349, 348])).
% 1.22/1.05  tff(351,plain,
% 1.22/1.05      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : refl((tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__comp_h_(A__questionmark_v1, A__questionmark_v2))) <=> (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__comp_h_(A__questionmark_v1, A__questionmark_v2))))),
% 1.22/1.05      inference(bind,[status(th)],[])).
% 1.22/1.05  tff(352,plain,
% 1.22/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__comp_h_(A__questionmark_v1, A__questionmark_v2))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__comp_h_(A__questionmark_v1, A__questionmark_v2)))),
% 1.22/1.05      inference(quant_intro,[status(thm)],[351])).
% 1.22/1.05  tff(353,plain,
% 1.22/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__comp_h_(A__questionmark_v1, A__questionmark_v2))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__comp_h_(A__questionmark_v1, A__questionmark_v2)))),
% 1.22/1.05      inference(rewrite,[status(thm)],[])).
% 1.22/1.05  tff(354,axiom,(![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__comp_h_(A__questionmark_v1, A__questionmark_v2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom32')).
% 1.22/1.05  tff(355,plain,
% 1.22/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__comp_h_(A__questionmark_v1, A__questionmark_v2)))),
% 1.22/1.05      inference(modus_ponens,[status(thm)],[354, 353])).
% 1.22/1.05  tff(356,plain,(
% 1.22/1.05      ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__comp_h_(A__questionmark_v1, A__questionmark_v2)))),
% 1.22/1.05      inference(skolemize,[status(sab)],[355])).
% 1.22/1.05  tff(357,plain,
% 1.22/1.05      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__comp_h_(A__questionmark_v1, A__questionmark_v2)))),
% 1.22/1.05      inference(modus_ponens,[status(thm)],[356, 352])).
% 1.22/1.05  tff(358,plain,
% 1.22/1.05      ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), tptp_fun__comp_h_(A__questionmark_v1, A__questionmark_v2)))) | (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))),
% 1.22/1.05      inference(quant_inst,[status(thm)],[])).
% 1.22/1.05  tff(359,plain,
% 1.22/1.05      (tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.05      inference(unit_resolution,[status(thm)],[358, 357])).
% 1.22/1.05  tff(360,plain,
% 1.22/1.05      (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__comp_l_(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|), tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))),
% 1.22/1.05      inference(symmetry,[status(thm)],[359])).
% 1.22/1.05  tff(361,plain,
% 1.22/1.05      (tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)),
% 1.22/1.06      inference(transitivity,[status(thm)],[360, 350])).
% 1.22/1.06  tff(362,plain,
% 1.22/1.06      (^[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$'] : refl(((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))),
% 1.22/1.06      inference(bind,[status(th)],[])).
% 1.22/1.06  tff(363,plain,
% 1.22/1.06      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'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$'] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.06      inference(quant_intro,[status(thm)],[362])).
% 1.22/1.06  tff(364,plain,
% 1.22/1.06      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) <=> (~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))), ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> (~(~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))))), rewrite((~(~((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))), ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))), (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (A__questionmark_v0 = A__questionmark_v2)) <=> (((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (A__questionmark_v0 = A__questionmark_v2)))), rewrite((((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))), (((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))),
% 1.22/1.06      inference(bind,[status(th)],[])).
% 1.22/1.06  tff(365,plain,
% 1.22/1.06      (![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$'] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (A__questionmark_v0 = A__questionmark_v2)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.06      inference(quant_intro,[status(thm)],[364])).
% 1.22/1.06  tff(366,plain,
% 1.22/1.06      (^[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$'|))) | (A__questionmark_v0 = A__questionmark_v2)) <=> ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (A__questionmark_v0 = A__questionmark_v2)))),
% 1.22/1.06      inference(bind,[status(th)],[])).
% 1.22/1.06  tff(367,plain,
% 1.22/1.06      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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$'] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (A__questionmark_v0 = A__questionmark_v2))),
% 1.22/1.06      inference(quant_intro,[status(thm)],[366])).
% 1.22/1.06  tff(368,plain,
% 1.22/1.06      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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$'|))) | (A__questionmark_v0 = A__questionmark_v2))),
% 1.22/1.06      inference(rewrite,[status(thm)],[])).
% 1.22/1.06  tff(369,plain,
% 1.22/1.06      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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)))),
% 1.22/1.06      inference(bind,[status(th)],[])).
% 1.22/1.06  tff(370,plain,
% 1.22/1.06      (![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))),
% 1.22/1.06      inference(quant_intro,[status(thm)],[369])).
% 1.22/1.06  tff(371,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$'|)) => (A__questionmark_v0 = A__questionmark_v2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom551')).
% 1.22/1.06  tff(372,plain,
% 1.22/1.06      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[371, 370])).
% 1.22/1.06  tff(373,plain,
% 1.22/1.06      (![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$'|))) | (A__questionmark_v0 = A__questionmark_v2))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[372, 368])).
% 1.22/1.06  tff(374,plain,
% 1.22/1.06      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (A__questionmark_v0 = A__questionmark_v2))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[373, 367])).
% 1.22/1.06  tff(375,plain,(
% 1.22/1.06      ![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$'] : ((~((tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)) & (tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (A__questionmark_v0 = A__questionmark_v2))),
% 1.22/1.06      inference(skolemize,[status(sab)],[374])).
% 1.22/1.06  tff(376,plain,
% 1.22/1.06      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[375, 365])).
% 1.22/1.06  tff(377,plain,
% 1.22/1.06      (![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$'] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[376, 363])).
% 1.22/1.06  tff(378,plain,
% 1.22/1.06      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | ((|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'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$'] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | (|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.06      inference(rewrite,[status(thm)],[])).
% 1.22/1.06  tff(379,plain,
% 1.22/1.06      (((|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | $false | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> ((|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.06      inference(rewrite,[status(thm)],[])).
% 1.22/1.06  tff(380,plain,
% 1.22/1.06      (((|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> ((|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | $false | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.06      inference(monotonicity,[status(thm)],[205])).
% 1.22/1.06  tff(381,plain,
% 1.22/1.06      (((|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> ((|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.06      inference(transitivity,[status(thm)],[380, 379])).
% 1.22/1.06  tff(382,plain,
% 1.22/1.06      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | ((|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'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$'] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | ((|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))),
% 1.22/1.06      inference(monotonicity,[status(thm)],[381])).
% 1.22/1.06  tff(383,plain,
% 1.22/1.06      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | ((|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'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$'] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | (|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.06      inference(transitivity,[status(thm)],[382, 378])).
% 1.22/1.06  tff(384,plain,
% 1.22/1.06      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | ((|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.06      inference(quant_inst,[status(thm)],[])).
% 1.22/1.06  tff(385,plain,
% 1.22/1.06      ((~![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$'] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | (|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[384, 383])).
% 1.22/1.06  tff(386,plain,
% 1.22/1.06      (|'i$'| = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))),
% 1.22/1.06      inference(unit_resolution,[status(thm)],[385, 377, 361])).
% 1.22/1.06  tff(387,plain,
% 1.22/1.06      (tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) = |'i$'|),
% 1.22/1.06      inference(symmetry,[status(thm)],[386])).
% 1.22/1.06  tff(388,plain,
% 1.22/1.06      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : 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))))),
% 1.22/1.06      inference(bind,[status(th)],[])).
% 1.22/1.06  tff(389,plain,
% 1.22/1.06      (![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)))),
% 1.22/1.06      inference(quant_intro,[status(thm)],[388])).
% 1.22/1.06  tff(390,plain,
% 1.22/1.06      (![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)))),
% 1.22/1.06      inference(rewrite,[status(thm)],[])).
% 1.22/1.06  tff(391,plain,
% 1.22/1.06      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : rewrite((tptp_fun__register_c_(A__questionmark_v0) => tptp_fun__clinear_c_(A__questionmark_v0)) <=> (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0))))),
% 1.22/1.06      inference(bind,[status(th)],[])).
% 1.22/1.06  tff(392,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (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$'] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 1.22/1.06      inference(quant_intro,[status(thm)],[391])).
% 1.22/1.06  tff(393,axiom,(![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__register_c_(A__questionmark_v0) => tptp_fun__clinear_c_(A__questionmark_v0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom57')).
% 1.22/1.06  tff(394,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[393, 392])).
% 1.22/1.06  tff(395,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[394, 390])).
% 1.22/1.06  tff(396,plain,(
% 1.22/1.06      ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 1.22/1.06      inference(skolemize,[status(sab)],[395])).
% 1.22/1.06  tff(397,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[396, 389])).
% 1.22/1.06  tff(398,plain,
% 1.22/1.06      (((~![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$'|) | (~tptp_fun__register_c_(|'j$'|)))),
% 1.22/1.06      inference(rewrite,[status(thm)],[])).
% 1.22/1.06  tff(399,plain,
% 1.22/1.06      ((~![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$'|)))),
% 1.22/1.06      inference(quant_inst,[status(thm)],[])).
% 1.22/1.06  tff(400,plain,
% 1.22/1.06      ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : (tptp_fun__clinear_c_(A__questionmark_v0) | (~tptp_fun__register_c_(A__questionmark_v0)))) | tptp_fun__clinear_c_(|'j$'|) | (~tptp_fun__register_c_(|'j$'|))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[399, 398])).
% 1.22/1.06  tff(401,plain,
% 1.22/1.06      (tptp_fun__clinear_c_(|'j$'|)),
% 1.22/1.06      inference(unit_resolution,[status(thm)],[400, 397, 276])).
% 1.22/1.06  tff(402,plain,
% 1.22/1.06      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : refl(((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))))) <=> ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (~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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))))))),
% 1.22/1.06      inference(bind,[status(th)],[])).
% 1.22/1.06  tff(403,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (~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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (~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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))),
% 1.22/1.06      inference(quant_intro,[status(thm)],[402])).
% 1.22/1.06  tff(404,plain,
% 1.22/1.06      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) <=> (~((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))))), ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) <=> (~(~((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))))))), rewrite((~(~((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))))) <=> ((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))))), ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) <=> ((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))))), rewrite((tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) <=> (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))))), (((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) | (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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) <=> (((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))))))), rewrite((((~tptp_fun__clinear_c_(A__questionmark_v0)) | (~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) | (~((~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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))))) <=> ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))), (((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) | (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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) <=> ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))))),
% 1.22/1.06      inference(bind,[status(th)],[])).
% 1.22/1.06  tff(405,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) | (tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (~tptp_fun__clinear_c_(A__questionmark_v0)) | (~((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(A__questionmark_v0)), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))),
% 1.22/1.06      inference(quant_intro,[status(thm)],[404])).
% 1.22/1.06  tff(406,plain,
% 1.22/1.06      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : 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$a'|))) <=> ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) | ?[A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))))),
% 1.22/1.06      inference(bind,[status(th)],[])).
% 1.22/1.06  tff(407,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(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, tptp_fun__collect_a_(|'top$c'|)))) | ?[A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))),
% 1.22/1.06      inference(quant_intro,[status(thm)],[406])).
% 1.22/1.06  tff(408,plain,
% 1.22/1.06      (![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'|)))),
% 1.22/1.06      inference(rewrite,[status(thm)],[])).
% 1.22/1.06  tff(409,plain,
% 1.22/1.06      (^[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$a'|))))),
% 1.22/1.06      inference(bind,[status(th)],[])).
% 1.22/1.06  tff(410,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((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$a'|)))),
% 1.22/1.06      inference(quant_intro,[status(thm)],[409])).
% 1.22/1.06  tff(411,axiom,(![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((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$a'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom532')).
% 1.22/1.06  tff(412,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(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$a'|)))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[411, 410])).
% 1.22/1.06  tff(413,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(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$a'|)))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[412, 408])).
% 1.22/1.06  tff(414,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) | ?[A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : (tptp_fun__clinear_b_(A__questionmark_v1) & (tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v1), A__questionmark_v0) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[413, 407])).
% 1.22/1.06  tff(415,plain,(
% 1.22/1.06      ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~(tptp_fun__clinear_c_(A__questionmark_v0) & tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|)))) | (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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))),
% 1.22/1.06      inference(skolemize,[status(sab)],[414])).
% 1.22/1.06  tff(416,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (~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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[415, 405])).
% 1.22/1.06  tff(417,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (~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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[416, 403])).
% 1.22/1.06  tff(418,plain,
% 1.22/1.06      (((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (~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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))) | ((~tptp_fun__inj_on_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|))) | (~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$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))) <=> ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (~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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))) | (~tptp_fun__inj_on_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|))) | (~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$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))),
% 1.22/1.06      inference(rewrite,[status(thm)],[])).
% 1.22/1.06  tff(419,plain,
% 1.22/1.06      ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (~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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))) | ((~tptp_fun__inj_on_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|))) | (~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$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))),
% 1.22/1.06      inference(quant_inst,[status(thm)],[])).
% 1.22/1.06  tff(420,plain,
% 1.22/1.06      ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ((~tptp_fun__inj_on_f_(A__questionmark_v0, tptp_fun__collect_a_(|'top$c'|))) | (~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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))))) | (~tptp_fun__inj_on_f_(|'j$'|, tptp_fun__collect_a_(|'top$c'|))) | (~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$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[419, 418])).
% 1.22/1.06  tff(421,plain,
% 1.22/1.06      (~((~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$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))))),
% 1.22/1.06      inference(unit_resolution,[status(thm)],[420, 417, 293, 401])).
% 1.22/1.06  tff(422,plain,
% 1.22/1.06      (((~tptp_fun__clinear_b_(tptp_fun_A__questionmark_v1_123(|'j$'|))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))) | (tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))),
% 1.22/1.06      inference(tautology,[status(thm)],[])).
% 1.22/1.06  tff(423,plain,
% 1.22/1.06      (tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)),
% 1.22/1.06      inference(unit_resolution,[status(thm)],[422, 421])).
% 1.22/1.06  tff(424,plain,
% 1.22/1.06      (((~![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$'] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))),
% 1.22/1.06      inference(rewrite,[status(thm)],[])).
% 1.22/1.06  tff(425,plain,
% 1.22/1.06      (((tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) <=> ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))),
% 1.22/1.06      inference(rewrite,[status(thm)],[])).
% 1.22/1.06  tff(426,plain,
% 1.22/1.06      (((~![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$'] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | ((tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | ((~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))))),
% 1.22/1.06      inference(monotonicity,[status(thm)],[425])).
% 1.22/1.06  tff(427,plain,
% 1.22/1.06      (((~![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$'] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | ((tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))))),
% 1.22/1.06      inference(transitivity,[status(thm)],[426, 424])).
% 1.22/1.06  tff(428,plain,
% 1.22/1.06      ((~![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$'] : ((A__questionmark_v0 = A__questionmark_v2) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | ((tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.06      inference(quant_inst,[status(thm)],[])).
% 1.22/1.06  tff(429,plain,
% 1.22/1.06      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', 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) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v1), A__questionmark_v2) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))) | (~(tptp_fun__fun_app_i_(tptp_fun__comp_b_(tptp_fun_A__questionmark_v1_123(|'j$'|)), |'j$'|) = tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[428, 427])).
% 1.22/1.06  tff(430,plain,
% 1.22/1.06      (tptp_fun_A__questionmark_v1_123(|'j$'|) = tptp_fun__comp_h_(|'i$'|, tptp_fun_A__questionmark_v1_118(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|)))),
% 1.22/1.06      inference(unit_resolution,[status(thm)],[429, 377, 423, 361])).
% 1.22/1.06  tff(431,plain,
% 1.22/1.06      (tptp_fun_A__questionmark_v1_123(|'j$'|) = |'i$'|),
% 1.22/1.06      inference(transitivity,[status(thm)],[430, 387])).
% 1.22/1.06  tff(432,plain,
% 1.22/1.06      (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun_A__questionmark_v1_123(|'j$'|)) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|)),
% 1.22/1.06      inference(monotonicity,[status(thm)],[431])).
% 1.22/1.06  tff(433,plain,
% 1.22/1.06      ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun_A__questionmark_v1_123(|'j$'|)) = |'g$'|) <=> (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|))),
% 1.22/1.06      inference(monotonicity,[status(thm)],[432, 234])).
% 1.22/1.06  tff(434,plain,
% 1.22/1.06      ((~(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun_A__questionmark_v1_123(|'j$'|)) = |'g$'|)) <=> (~(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)))),
% 1.22/1.06      inference(monotonicity,[status(thm)],[433])).
% 1.22/1.06  tff(435,plain,
% 1.22/1.06      (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun_A__questionmark_v1_123(|'j$'|))),
% 1.22/1.06      inference(symmetry,[status(thm)],[432])).
% 1.22/1.06  tff(436,plain,
% 1.22/1.06      (tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)) = tptp_fun__comp__(tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.22/1.06      inference(monotonicity,[status(thm)],[246])).
% 1.22/1.06  tff(437,plain,
% 1.22/1.06      (tptp_fun__comp__(tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))) = tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|))),
% 1.22/1.06      inference(symmetry,[status(thm)],[436])).
% 1.22/1.06  tff(438,plain,
% 1.22/1.06      (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|)),
% 1.22/1.06      inference(monotonicity,[status(thm)],[437])).
% 1.22/1.06  tff(439,plain,
% 1.22/1.06      (tptp_fun__comp__(|'f$'|) = tptp_fun__comp__(tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|)))),
% 1.22/1.06      inference(monotonicity,[status(thm)],[312])).
% 1.22/1.06  tff(440,plain,
% 1.22/1.06      (tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_n_(|'f$'|, tptp_fun__fun_app_i_(tptp_fun__comp_b_(|'i$'|), |'j$'|))), |'i$'|)),
% 1.22/1.06      inference(monotonicity,[status(thm)],[439])).
% 1.22/1.06  tff(441,plain,
% 1.22/1.06      (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$'|), |'i$'|), |'j$'|)), tptp_fun_A__questionmark_v1_123(|'j$'|))),
% 1.22/1.06      inference(transitivity,[status(thm)],[440, 438, 435])).
% 1.22/1.06  tff(442,plain,
% 1.22/1.06      ((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$'|), |'j$'|)), tptp_fun_A__questionmark_v1_123(|'j$'|)) = |'g$'|)),
% 1.22/1.06      inference(monotonicity,[status(thm)],[441])).
% 1.22/1.06  tff(443,plain,
% 1.22/1.06      ((~(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$'|), |'j$'|)), tptp_fun_A__questionmark_v1_123(|'j$'|)) = |'g$'|))),
% 1.22/1.06      inference(monotonicity,[status(thm)],[442])).
% 1.22/1.06  tff(444,plain,
% 1.22/1.06      ((~(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = |'g$'|)) <=> (~(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = |'g$'|))),
% 1.22/1.06      inference(rewrite,[status(thm)],[])).
% 1.22/1.06  tff(445,axiom,(~(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = |'g$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture1')).
% 1.22/1.06  tff(446,plain,
% 1.22/1.06      (~(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|) = |'g$'|)),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[445, 444])).
% 1.22/1.06  tff(447,plain,
% 1.22/1.06      (~(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun_A__questionmark_v1_123(|'j$'|)) = |'g$'|)),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[446, 443])).
% 1.22/1.06  tff(448,plain,
% 1.22/1.06      (~(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|))),
% 1.22/1.06      inference(modus_ponens,[status(thm)],[447, 434])).
% 1.22/1.06  tff(449,plain,
% 1.22/1.06      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : refl(((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) <=> ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))))),
% 1.22/1.06      inference(bind,[status(th)],[])).
% 1.22/1.06  tff(450,plain,
% 1.22/1.06      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))),
% 1.22/1.07      inference(quant_intro,[status(thm)],[449])).
% 1.22/1.07  tff(451,plain,
% 1.22/1.07      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : trans(monotonicity(trans(monotonicity(rewrite(((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)) <=> (~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))))), ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) <=> (~(~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))))))), rewrite((~(~((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))))) <=> ((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))), ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) <=> ((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))))), (((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3))) <=> (((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3))))), rewrite((((~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3))) <=> ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))), (((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3))) <=> ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))))),
% 1.22/1.07      inference(bind,[status(th)],[])).
% 1.22/1.07  tff(452,plain,
% 1.22/1.07      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))),
% 1.22/1.07      inference(quant_intro,[status(thm)],[451])).
% 1.22/1.07  tff(453,plain,
% 1.22/1.07      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)))),
% 1.22/1.07      inference(rewrite,[status(thm)],[])).
% 1.22/1.07  tff(454,plain,
% 1.22/1.07      (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : rewrite((((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)) => (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3))) <=> ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3))))),
% 1.22/1.07      inference(bind,[status(th)],[])).
% 1.22/1.07  tff(455,plain,
% 1.22/1.07      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : (((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)) => (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)))),
% 1.22/1.07      inference(quant_intro,[status(thm)],[454])).
% 1.22/1.07  tff(456,axiom,(![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : (((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)) => (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom595')).
% 1.22/1.07  tff(457,plain,
% 1.22/1.07      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)))),
% 1.22/1.07      inference(modus_ponens,[status(thm)],[456, 455])).
% 1.22/1.07  tff(458,plain,
% 1.22/1.07      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)))),
% 1.22/1.07      inference(modus_ponens,[status(thm)],[457, 453])).
% 1.22/1.07  tff(459,plain,(
% 1.22/1.07      ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3)) & (tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)))),
% 1.22/1.07      inference(skolemize,[status(sab)],[458])).
% 1.22/1.07  tff(460,plain,
% 1.22/1.07      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))),
% 1.22/1.07      inference(modus_ponens,[status(thm)],[459, 452])).
% 1.22/1.07  tff(461,plain,
% 1.22/1.07      (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))),
% 1.22/1.07      inference(modus_ponens,[status(thm)],[460, 450])).
% 1.22/1.07  tff(462,plain,
% 1.22/1.07      (((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))) | ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|))))) <=> ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|))))),
% 1.22/1.07      inference(rewrite,[status(thm)],[])).
% 1.22/1.07  tff(463,plain,
% 1.22/1.07      (((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | $false | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)))) <=> ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|))))),
% 1.22/1.07      inference(rewrite,[status(thm)],[])).
% 1.22/1.07  tff(464,plain,
% 1.22/1.07      (((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)))) <=> ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | $false | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|))))),
% 1.22/1.07      inference(monotonicity,[status(thm)],[202])).
% 1.22/1.07  tff(465,plain,
% 1.22/1.07      (((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)))) <=> ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|))))),
% 1.22/1.07      inference(transitivity,[status(thm)],[464, 463])).
% 1.22/1.07  tff(466,plain,
% 1.22/1.07      (((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))) | ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|))))) <=> ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))) | ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)))))),
% 1.22/1.07      inference(monotonicity,[status(thm)],[465])).
% 1.22/1.07  tff(467,plain,
% 1.22/1.07      (((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))) | ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|))))) <=> ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|))))),
% 1.22/1.07      inference(transitivity,[status(thm)],[466, 462])).
% 1.22/1.07  tff(468,plain,
% 1.22/1.07      ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))) | ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(|'j$'|), |'i$'|))) | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|))))),
% 1.22/1.07      inference(quant_inst,[status(thm)],[])).
% 1.22/1.07  tff(469,plain,
% 1.22/1.07      ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$', A__questionmark_v3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v4: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v5: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v0)), A__questionmark_v1) = tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v5), A__questionmark_v3)) | (~(tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_f_(tptp_fun__comp_a_(A__questionmark_v2), A__questionmark_v3))) | (~(tptp_fun__comp_k_(A__questionmark_v4, A__questionmark_v2) = A__questionmark_v5)))) | (tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)))),
% 1.22/1.07      inference(modus_ponens,[status(thm)],[468, 467])).
% 1.22/1.07  tff(470,plain,
% 1.22/1.07      ((tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|) = tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|)) | (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)))),
% 1.22/1.07      inference(unit_resolution,[status(thm)],[469, 461])).
% 1.22/1.07  tff(471,plain,
% 1.22/1.07      (~(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|))),
% 1.22/1.07      inference(unit_resolution,[status(thm)],[470, 448])).
% 1.22/1.07  tff(472,plain,
% 1.22/1.07      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : refl(((A__questionmark_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)))))) <=> ((A__questionmark_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)))))))),
% 1.22/1.07      inference(bind,[status(th)],[])).
% 1.22/1.07  tff(473,plain,
% 1.22/1.07      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((A__questionmark_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)))))) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', 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_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0))))))),
% 1.22/1.07      inference(quant_intro,[status(thm)],[472])).
% 1.22/1.07  tff(474,plain,
% 1.22/1.07      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : rewrite((((~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)))))) | (A__questionmark_v2 = A__questionmark_v3)) <=> ((A__questionmark_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)))))))),
% 1.22/1.07      inference(bind,[status(th)],[])).
% 1.22/1.07  tff(475,plain,
% 1.22/1.07      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : (((~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)))))) | (A__questionmark_v2 = A__questionmark_v3)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', 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_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0))))))),
% 1.22/1.07      inference(quant_intro,[status(thm)],[474])).
% 1.22/1.07  tff(476,plain,
% 1.22/1.07      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : rewrite(((~((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4))))) | (A__questionmark_v2 = A__questionmark_v3)) <=> ((~((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|)) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4))))) | (A__questionmark_v2 = A__questionmark_v3)))),
% 1.22/1.07      inference(bind,[status(th)],[])).
% 1.22/1.07  tff(477,plain,
% 1.22/1.07      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4))))) | (A__questionmark_v2 = A__questionmark_v3)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|)) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4))))) | (A__questionmark_v2 = A__questionmark_v3))),
% 1.22/1.07      inference(quant_intro,[status(thm)],[476])).
% 1.22/1.07  tff(478,plain,
% 1.22/1.07      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4))))) | (A__questionmark_v2 = A__questionmark_v3)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4))))) | (A__questionmark_v2 = A__questionmark_v3))),
% 1.22/1.07      inference(rewrite,[status(thm)],[])).
% 1.22/1.07  tff(479,plain,
% 1.22/1.07      (^[A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : trans(monotonicity(rewrite(((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1) => (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4)))) <=> ((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4))))), ((((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1) => (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4)))) => (A__questionmark_v2 = A__questionmark_v3)) <=> (((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4)))) => (A__questionmark_v2 = A__questionmark_v3)))), rewrite((((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4)))) => (A__questionmark_v2 = A__questionmark_v3)) <=> ((~((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4))))) | (A__questionmark_v2 = A__questionmark_v3))), ((((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1) => (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4)))) => (A__questionmark_v2 = A__questionmark_v3)) <=> ((~((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4))))) | (A__questionmark_v2 = A__questionmark_v3))))),
% 1.22/1.07      inference(bind,[status(th)],[])).
% 1.22/1.07  tff(480,plain,
% 1.22/1.07      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : (((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1) => (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4)))) => (A__questionmark_v2 = A__questionmark_v3)) <=> ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4))))) | (A__questionmark_v2 = A__questionmark_v3))),
% 1.22/1.07      inference(quant_intro,[status(thm)],[479])).
% 1.22/1.07  tff(481,axiom,(![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : (((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : (tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1) => (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4)))) => (A__questionmark_v2 = A__questionmark_v3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom385')).
% 1.22/1.07  tff(482,plain,
% 1.22/1.07      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4))))) | (A__questionmark_v2 = A__questionmark_v3))),
% 1.22/1.07      inference(modus_ponens,[status(thm)],[481, 480])).
% 1.22/1.07  tff(483,plain,
% 1.22/1.07      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = |'top$'|) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4))))) | (A__questionmark_v2 = A__questionmark_v3))),
% 1.22/1.07      inference(modus_ponens,[status(thm)],[482, 478])).
% 1.22/1.07  tff(484,plain,
% 1.22/1.07      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((~((tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|)) & ![A__questionmark_v4: 'B_ell2_b_ell2_cblinfun$'] : ((~tptp_fun__member_b_(A__questionmark_v4, A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v4) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), A__questionmark_v4))))) | (A__questionmark_v2 = A__questionmark_v3))),
% 1.22/1.07      inference(modus_ponens,[status(thm)],[483, 477])).
% 1.22/1.07  tff(485,plain,(
% 1.22/1.07      ![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : (((~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)))))) | (A__questionmark_v2 = A__questionmark_v3))),
% 1.22/1.07      inference(skolemize,[status(sab)],[484])).
% 1.22/1.07  tff(486,plain,
% 1.22/1.07      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', 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_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0))))))),
% 1.22/1.07      inference(modus_ponens,[status(thm)],[485, 475])).
% 1.22/1.07  tff(487,plain,
% 1.22/1.07      (![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : ((A__questionmark_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0))))))),
% 1.22/1.07      inference(modus_ponens,[status(thm)],[486, 473])).
% 1.22/1.07  tff(488,plain,
% 1.22/1.07      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', 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_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0))))))) | ((~(tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))))) <=> ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', 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_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0))))))) | (~(tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))))),
% 1.22/1.07      inference(rewrite,[status(thm)],[])).
% 1.22/1.07  tff(489,plain,
% 1.22/1.07      (((tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)) | (~(tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))))) <=> ((~(tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))))),
% 1.22/1.07      inference(rewrite,[status(thm)],[])).
% 1.22/1.07  tff(490,plain,
% 1.22/1.07      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', 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_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0))))))) | ((tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)) | (~(tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))))) <=> ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', 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_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0))))))) | ((~(tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))))))),
% 1.22/1.07      inference(monotonicity,[status(thm)],[489])).
% 1.22/1.07  tff(491,plain,
% 1.22/1.07      (((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', 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_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0))))))) | ((tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)) | (~(tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))))) <=> ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', 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_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0))))))) | (~(tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))))),
% 1.22/1.07      inference(transitivity,[status(thm)],[490, 488])).
% 1.22/1.07  tff(492,plain,
% 1.22/1.07      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', 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_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0))))))) | ((tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)) | (~(tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))))),
% 1.22/1.07      inference(quant_inst,[status(thm)],[])).
% 1.22/1.07  tff(493,plain,
% 1.22/1.07      ((~![A__questionmark_v0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun_set$', 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_v2 = A__questionmark_v3) | (~(tptp_fun__image_e_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__collect_a_(|'top$c'|))) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v2), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(A__questionmark_v3), A__questionmark_v0), tptp_fun_A__questionmark_v4_100(A__questionmark_v3, A__questionmark_v2, A__questionmark_v1, A__questionmark_v0))))))) | (~(tptp_fun__image_e_(|'i$'|, tptp_fun__collect_b_(|'top$d'|)) = tptp_fun__collect_a_(|'top$c'|))) | (tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))))),
% 1.22/1.08      inference(modus_ponens,[status(thm)],[492, 491])).
% 1.22/1.08  tff(494,plain,
% 1.22/1.08      ((tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|) = tptp_fun__comp_k_(|'g$'|, |'j$'|)) | (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))))),
% 1.22/1.08      inference(unit_resolution,[status(thm)],[493, 487, 68])).
% 1.22/1.08  tff(495,plain,
% 1.22/1.08      (~((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))),
% 1.22/1.08      inference(unit_resolution,[status(thm)],[494, 471])).
% 1.22/1.08  tff(496,plain,
% 1.22/1.08      (((~tptp_fun__member_b_(tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|), tptp_fun__collect_b_(|'top$d'|))) | (tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))) | (~(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))),
% 1.22/1.08      inference(tautology,[status(thm)],[])).
% 1.22/1.08  tff(497,plain,
% 1.22/1.08      (~(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))),
% 1.22/1.08      inference(unit_resolution,[status(thm)],[496, 495])).
% 1.22/1.08  tff(498,plain,
% 1.22/1.08      (~(tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))),
% 1.22/1.08      inference(modus_ponens,[status(thm)],[497, 323])).
% 1.22/1.08  tff(499,plain,
% 1.22/1.08      (^[A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : refl(((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)) <=> ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)))),
% 1.22/1.08      inference(bind,[status(th)],[])).
% 1.22/1.08  tff(500,plain,
% 1.22/1.08      (![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)) <=> ![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 1.22/1.08      inference(quant_intro,[status(thm)],[499])).
% 1.22/1.08  tff(501,plain,
% 1.22/1.08      (![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)) <=> ![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 1.22/1.08      inference(rewrite,[status(thm)],[])).
% 1.22/1.08  tff(502,plain,
% 1.22/1.08      (^[A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : rewrite((tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2)) => (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)) <=> ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)))),
% 1.22/1.08      inference(bind,[status(th)],[])).
% 1.22/1.08  tff(503,plain,
% 1.22/1.08      (![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : (tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2)) => (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0)) <=> ![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 1.22/1.08      inference(quant_intro,[status(thm)],[502])).
% 1.22/1.08  tff(504,axiom,(![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : (tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2)) => (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom341')).
% 1.22/1.08  tff(505,plain,
% 1.22/1.08      (![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 1.22/1.08      inference(modus_ponens,[status(thm)],[504, 503])).
% 1.22/1.08  tff(506,plain,
% 1.22/1.08      (![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 1.22/1.08      inference(modus_ponens,[status(thm)],[505, 501])).
% 1.22/1.08  tff(507,plain,(
% 1.22/1.08      ![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 1.22/1.08      inference(skolemize,[status(sab)],[506])).
% 1.22/1.08  tff(508,plain,
% 1.22/1.08      (![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))),
% 1.22/1.08      inference(modus_ponens,[status(thm)],[507, 500])).
% 1.22/1.08  tff(509,plain,
% 1.22/1.08      (((~![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))) | ((~tptp_fun__member__(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)), tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_a_(|'top$c'|)))) | (tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))) <=> ((~![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))) | (~tptp_fun__member__(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)), tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_a_(|'top$c'|)))) | (tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))),
% 1.22/1.08      inference(rewrite,[status(thm)],[])).
% 1.22/1.08  tff(510,plain,
% 1.22/1.08      ((~![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))) | ((~tptp_fun__member__(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)), tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_a_(|'top$c'|)))) | (tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|))))),
% 1.22/1.08      inference(quant_inst,[status(thm)],[])).
% 1.22/1.08  tff(511,plain,
% 1.22/1.08      ((~![A__questionmark_v0: 'C_ell2_c_ell2_cblinfun$', A__questionmark_v1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$', A__questionmark_v2: 'A_ell2_a_ell2_cblinfun_set$'] : ((~tptp_fun__member__(A__questionmark_v0, tptp_fun__image__(A__questionmark_v1, A__questionmark_v2))) | (tptp_fun__fun_app_c_(A__questionmark_v1, tptp_fun__fun_app_l_(tptp_fun__inv_into__(A__questionmark_v2, A__questionmark_v1), A__questionmark_v0)) = A__questionmark_v0))) | (~tptp_fun__member__(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)), tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_a_(|'top$c'|)))) | (tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))),
% 1.22/1.08      inference(modus_ponens,[status(thm)],[510, 509])).
% 1.24/1.11  tff(512,plain,
% 1.24/1.11      ((~tptp_fun__member__(tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)), tptp_fun__image__(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_a_(|'top$c'|)))) | (tptp_fun__fun_app_c_(tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__fun_app_l_(tptp_fun__inv_into__(tptp_fun__collect_a_(|'top$c'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|)), tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))) = tptp_fun__fun_app_b_(tptp_fun__fun_app_a_(tptp_fun__comp__(tptp_fun__comp_k_(|'g$'|, |'j$'|)), |'i$'|), tptp_fun_A__questionmark_v4_100(tptp_fun__comp_k_(|'g$'|, |'j$'|), tptp_fun__comp_k_(tptp_fun__fun_app_a_(tptp_fun__comp__(|'f$'|), |'i$'|), |'j$'|), tptp_fun__collect_b_(|'top$d'|), |'i$'|)))),
% 1.24/1.11      inference(unit_resolution,[status(thm)],[511, 508])).
% 1.24/1.11  tff(513,plain,
% 1.24/1.11      ($false),
% 1.24/1.11      inference(unit_resolution,[status(thm)],[512, 498, 157])).
% 1.24/1.11  % SZS output end Proof
%------------------------------------------------------------------------------