TSTP Solution File: ITP004+1 by Z3---4.8.9.0

View Problem - Process Solution 
%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ITP004+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% 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 04:14:38 EDT 2022

% Result   : Theorem 0.18s 0.40s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : ITP004+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.11/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n014.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu Sep  1 01:53:32 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.18/0.33  Usage: tptp [options] [-file:]file
% 0.18/0.33    -h, -?       prints this message.
% 0.18/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.18/0.33    -m, -model   generate model.
% 0.18/0.33    -p, -proof   generate proof.
% 0.18/0.33    -c, -core    generate unsat core of named formulas.
% 0.18/0.33    -st, -statistics display statistics.
% 0.18/0.33    -t:timeout   set timeout (in second).
% 0.18/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.18/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.18/0.33    -<param>:<value> configuration parameter and value.
% 0.18/0.33    -o:<output-file> file to place output in.
% 0.18/0.40  % SZS status Theorem
% 0.18/0.40  % SZS output start Proof
% 0.18/0.40  tff(p_type, type, (
% 0.18/0.40     p: $i > $o)).
% 0.18/0.40  tff(s_type, type, (
% 0.18/0.40     s: ( $i * $i ) > $i)).
% 0.18/0.40  tff(c_2Ebool_2EIN_2E2_type, type, (
% 0.18/0.40     c_2Ebool_2EIN_2E2: ( $i * $i ) > $i)).
% 0.18/0.40  tff(c_2Epred__set_2EDELETE_2E2_type, type, (
% 0.18/0.40     c_2Epred__set_2EDELETE_2E2: ( $i * $i ) > $i)).
% 0.18/0.40  tff(c_2Epred__set_2ECHOICE_2E1_type, type, (
% 0.18/0.40     c_2Epred__set_2ECHOICE_2E1: $i > $i)).
% 0.18/0.40  tff(tptp_fun_V0s_2E0_4_type, type, (
% 0.18/0.40     tptp_fun_V0s_2E0_4: $i)).
% 0.18/0.40  tff(tyop_2Emin_2Efun_type, type, (
% 0.18/0.40     tyop_2Emin_2Efun: ( $i * $i ) > $i)).
% 0.18/0.40  tff(tyop_2Emin_2Ebool_type, type, (
% 0.18/0.40     tyop_2Emin_2Ebool: $i)).
% 0.18/0.40  tff(tptp_fun_A_27a_5_type, type, (
% 0.18/0.40     tptp_fun_A_27a_5: $i)).
% 0.18/0.40  tff(tptp_fun_V2x_2E0_3_type, type, (
% 0.18/0.40     tptp_fun_V2x_2E0_3: ( $i * $i * $i ) > $i)).
% 0.18/0.40  tff(c_2Epred__set_2EREST_2E1_type, type, (
% 0.18/0.40     c_2Epred__set_2EREST_2E1: $i > $i)).
% 0.18/0.40  tff(c_2Ebool_2ET_2E0_type, type, (
% 0.18/0.40     c_2Ebool_2ET_2E0: $i)).
% 0.18/0.40  tff(c_2Epred__set_2ESUBSET_2E2_type, type, (
% 0.18/0.40     c_2Epred__set_2ESUBSET_2E2: ( $i * $i ) > $i)).
% 0.18/0.40  tff(1,plain,
% 0.18/0.40      (^[A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : rewrite((~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))) <=> (~((~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))),
% 0.18/0.40      inference(bind,[status(th)],[])).
% 0.18/0.40  tff(2,plain,
% 0.18/0.40      (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))) <=> ![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))),
% 0.18/0.41      inference(quant_intro,[status(thm)],[1])).
% 0.18/0.41  tff(3,plain,
% 0.18/0.41      (^[A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : refl((~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))) <=> (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))))),
% 0.18/0.41      inference(bind,[status(th)],[])).
% 0.18/0.41  tff(4,plain,
% 0.18/0.41      (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))) <=> ![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))),
% 0.18/0.41      inference(quant_intro,[status(thm)],[3])).
% 0.18/0.41  tff(5,plain,
% 0.18/0.41      (^[A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : rewrite((~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))) <=> (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))))),
% 0.18/0.41      inference(bind,[status(th)],[])).
% 0.18/0.41  tff(6,plain,
% 0.18/0.41      (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))) <=> ![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))),
% 0.18/0.41      inference(quant_intro,[status(thm)],[5])).
% 0.18/0.41  tff(7,plain,
% 0.18/0.41      (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))) <=> ![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))),
% 0.18/0.41      inference(transitivity,[status(thm)],[6, 4])).
% 0.18/0.41  tff(8,plain,
% 0.18/0.41      (^[A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : trans(monotonicity(rewrite(((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))) <=> ((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))), ((((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))) & (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) <=> (((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))) & (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))), rewrite((((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))) & (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) <=> (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))), ((((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))) & (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) <=> (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))))),
% 0.18/0.41      inference(bind,[status(th)],[])).
% 0.18/0.41  tff(9,plain,
% 0.18/0.41      (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))) & (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) <=> ![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))),
% 0.18/0.41      inference(quant_intro,[status(thm)],[8])).
% 0.18/0.41  tff(10,plain,
% 0.18/0.41      (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) <=> ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))) <=> ![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) <=> ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))),
% 0.18/0.41      inference(rewrite,[status(thm)],[])).
% 0.18/0.41  tff(11,plain,
% 0.18/0.41      (^[A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : rewrite((p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) <=> ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))) => p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) <=> ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))),
% 0.18/0.42      inference(bind,[status(th)],[])).
% 0.18/0.42  tff(12,plain,
% 0.18/0.42      (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) <=> ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))) => p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) <=> ![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) <=> ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))),
% 0.18/0.42      inference(quant_intro,[status(thm)],[11])).
% 0.18/0.42  tff(13,axiom,(![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) <=> ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))) => p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm_2Epred__set_2ESUBSET__DEF')).
% 0.18/0.42  tff(14,plain,
% 0.18/0.42      (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) <=> ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))),
% 0.18/0.42      inference(modus_ponens,[status(thm)],[13, 12])).
% 0.18/0.42  tff(15,plain,
% 0.18/0.42      (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) <=> ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))),
% 0.18/0.42      inference(modus_ponens,[status(thm)],[14, 10])).
% 0.18/0.42  tff(16,plain,(
% 0.18/0.42      ![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))) & (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))),
% 0.18/0.42      inference(skolemize,[status(sab)],[15])).
% 0.18/0.42  tff(17,plain,
% 0.18/0.42      (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))),
% 0.18/0.42      inference(modus_ponens,[status(thm)],[16, 9])).
% 0.18/0.42  tff(18,plain,
% 0.18/0.42      (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))),
% 0.18/0.42      inference(modus_ponens,[status(thm)],[17, 7])).
% 0.18/0.42  tff(19,plain,
% 0.18/0.42      (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))),
% 0.18/0.42      inference(modus_ponens,[status(thm)],[18, 2])).
% 0.18/0.42  tff(20,plain,
% 0.18/0.42      ((~![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))) | (~((~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | (~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))))),
% 0.18/0.42      inference(quant_inst,[status(thm)],[])).
% 0.18/0.42  tff(21,plain,
% 0.18/0.42      (~((~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | (~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))),
% 0.18/0.42      inference(unit_resolution,[status(thm)],[20, 19])).
% 0.18/0.42  tff(22,plain,
% 0.18/0.42      (((~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | (~((~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | ![V2x_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))),
% 0.18/0.42      inference(tautology,[status(thm)],[])).
% 0.18/0.42  tff(23,plain,
% 0.18/0.42      (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))),
% 0.18/0.42      inference(unit_resolution,[status(thm)],[22, 21])).
% 0.18/0.42  tff(24,plain,
% 0.18/0.42      ((~![A_27a: $i, V0s_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) <=> (~![A_27a: $i, V0s_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))),
% 0.18/0.42      inference(rewrite,[status(thm)],[])).
% 0.18/0.42  tff(25,axiom,(~![A_27a: $i, V0s_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm_2Epred__set_2EREST__SUBSET')).
% 0.18/0.42  tff(26,plain,
% 0.18/0.42      (~![A_27a: $i, V0s_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))),
% 0.18/0.42      inference(modus_ponens,[status(thm)],[25, 24])).
% 0.18/0.42  tff(27,plain,
% 0.18/0.42      (~![A_27a: $i, V0s_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[26, 24])).
% 0.18/0.43  tff(28,plain,
% 0.18/0.43      (~![A_27a: $i, V0s_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[27, 24])).
% 0.18/0.43  tff(29,plain,
% 0.18/0.43      (~![A_27a: $i, V0s_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[28, 24])).
% 0.18/0.43  tff(30,plain,
% 0.18/0.43      (~![A_27a: $i, V0s_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[29, 24])).
% 0.18/0.43  tff(31,plain,
% 0.18/0.43      (~![A_27a: $i, V0s_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[30, 24])).
% 0.18/0.43  tff(32,plain,
% 0.18/0.43      (~![A_27a: $i, V0s_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[31, 24])).
% 0.18/0.43  tff(33,plain,(
% 0.18/0.43      ~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))),
% 0.18/0.43      inference(skolemize,[status(sab)],[32])).
% 0.18/0.43  tff(34,plain,
% 0.18/0.43      ((~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))),
% 0.18/0.43      inference(tautology,[status(thm)],[])).
% 0.18/0.43  tff(35,plain,
% 0.18/0.43      ((~(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))),
% 0.18/0.43      inference(unit_resolution,[status(thm)],[34, 33])).
% 0.18/0.43  tff(36,plain,
% 0.18/0.43      (~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))),
% 0.18/0.43      inference(unit_resolution,[status(thm)],[35, 23])).
% 0.18/0.43  tff(37,plain,
% 0.18/0.43      ((p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) | p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))),
% 0.18/0.43      inference(tautology,[status(thm)],[])).
% 0.18/0.43  tff(38,plain,
% 0.18/0.43      (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))),
% 0.18/0.43      inference(unit_resolution,[status(thm)],[37, 36])).
% 0.18/0.43  tff(39,plain,
% 0.18/0.43      (p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)) <=> p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))),
% 0.18/0.43      inference(rewrite,[status(thm)],[])).
% 0.18/0.43  tff(40,axiom,(p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reserved_2Eho_2Etruth')).
% 0.18/0.43  tff(41,plain,
% 0.18/0.43      (p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.43  tff(42,plain,
% 0.18/0.43      ((~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))) <=> p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))),
% 0.18/0.43      inference(tautology,[status(thm)],[])).
% 0.18/0.43  tff(43,plain,
% 0.18/0.43      (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))) <=> p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))),
% 0.18/0.43      inference(unit_resolution,[status(thm)],[42, 41, 38])).
% 0.18/0.43  tff(44,plain,
% 0.18/0.43      (^[V0_2E0: $i, V1_2E0: $i] : refl(((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) <=> ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))))),
% 0.18/0.43      inference(bind,[status(th)],[])).
% 0.18/0.43  tff(45,plain,
% 0.18/0.43      (![V0_2E0: $i, V1_2E0: $i] : ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) <=> ![V0_2E0: $i, V1_2E0: $i] : ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))))),
% 0.18/0.43      inference(quant_intro,[status(thm)],[44])).
% 0.18/0.43  tff(46,plain,
% 0.18/0.43      (![V0_2E0: $i, V1_2E0: $i] : ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) <=> ![V0_2E0: $i, V1_2E0: $i] : ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))))),
% 0.18/0.43      inference(rewrite,[status(thm)],[])).
% 0.18/0.43  tff(47,plain,
% 0.18/0.43      (^[V0_2E0: $i, V1_2E0: $i] : rewrite(((p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))) => (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0))) <=> ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))))),
% 0.18/0.43      inference(bind,[status(th)],[])).
% 0.18/0.43  tff(48,plain,
% 0.18/0.43      (![V0_2E0: $i, V1_2E0: $i] : ((p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))) => (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0))) <=> ![V0_2E0: $i, V1_2E0: $i] : ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))))),
% 0.18/0.43      inference(quant_intro,[status(thm)],[47])).
% 0.18/0.43  tff(49,axiom,(![V0_2E0: $i, V1_2E0: $i] : ((p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))) => (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reserved_2Eho_2Eboolext')).
% 0.18/0.43  tff(50,plain,
% 0.18/0.43      (![V0_2E0: $i, V1_2E0: $i] : ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.43  tff(51,plain,
% 0.18/0.43      (![V0_2E0: $i, V1_2E0: $i] : ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[50, 46])).
% 0.18/0.43  tff(52,plain,(
% 0.18/0.43      ![V0_2E0: $i, V1_2E0: $i] : ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))))),
% 0.18/0.43      inference(skolemize,[status(sab)],[51])).
% 0.18/0.43  tff(53,plain,
% 0.18/0.43      (![V0_2E0: $i, V1_2E0: $i] : ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[52, 45])).
% 0.18/0.43  tff(54,plain,
% 0.18/0.43      (((~![V0_2E0: $i, V1_2E0: $i] : ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))))) | ((s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) = s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)) | ((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))) <=> p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))))) <=> ((~![V0_2E0: $i, V1_2E0: $i] : ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))))) | (s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) = s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)) | ((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))) <=> p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))))),
% 0.18/0.43      inference(rewrite,[status(thm)],[])).
% 0.18/0.43  tff(55,plain,
% 0.18/0.43      ((~![V0_2E0: $i, V1_2E0: $i] : ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))))) | ((s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) = s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)) | ((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))) <=> p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))))),
% 0.18/0.43      inference(quant_inst,[status(thm)],[])).
% 0.18/0.43  tff(56,plain,
% 0.18/0.43      ((~![V0_2E0: $i, V1_2E0: $i] : ((s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)) | ((~p(s(tyop_2Emin_2Ebool, V0_2E0))) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))))) | (s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) = s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)) | ((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))) <=> p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.43  tff(57,plain,
% 0.18/0.43      (s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) = s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)),
% 0.18/0.44      inference(unit_resolution,[status(thm)],[56, 53, 43])).
% 0.18/0.44  tff(58,plain,
% 0.18/0.44      (^[A_27a: $i, V0s_2E0: $i] : refl((s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) <=> (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))),
% 0.18/0.44      inference(bind,[status(th)],[])).
% 0.18/0.44  tff(59,plain,
% 0.18/0.44      (![A_27a: $i, V0s_2E0: $i] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) <=> ![A_27a: $i, V0s_2E0: $i] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))),
% 0.18/0.44      inference(quant_intro,[status(thm)],[58])).
% 0.18/0.44  tff(60,plain,
% 0.18/0.44      (![A_27a: $i, V0s_2E0: $i] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) <=> ![A_27a: $i, V0s_2E0: $i] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))),
% 0.18/0.44      inference(rewrite,[status(thm)],[])).
% 0.18/0.44  tff(61,axiom,(![A_27a: $i, V0s_2E0: $i] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm_2Epred__set_2EREST__DEF')).
% 0.18/0.44  tff(62,plain,
% 0.18/0.44      (![A_27a: $i, V0s_2E0: $i] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))),
% 0.18/0.44      inference(modus_ponens,[status(thm)],[61, 60])).
% 0.18/0.44  tff(63,plain,(
% 0.18/0.44      ![A_27a: $i, V0s_2E0: $i] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))),
% 0.18/0.44      inference(skolemize,[status(sab)],[62])).
% 0.18/0.44  tff(64,plain,
% 0.18/0.44      (![A_27a: $i, V0s_2E0: $i] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))),
% 0.18/0.44      inference(modus_ponens,[status(thm)],[63, 59])).
% 0.18/0.44  tff(65,plain,
% 0.18/0.44      ((~![A_27a: $i, V0s_2E0: $i] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))) | (s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))) = s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))),
% 0.18/0.44      inference(quant_inst,[status(thm)],[])).
% 0.18/0.44  tff(66,plain,
% 0.18/0.44      (s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))) = s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))),
% 0.18/0.44      inference(unit_resolution,[status(thm)],[65, 64])).
% 0.18/0.44  tff(67,plain,
% 0.18/0.44      (s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) = s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))),
% 0.18/0.44      inference(symmetry,[status(thm)],[66])).
% 0.18/0.44  tff(68,plain,
% 0.18/0.44      (c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) = c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))),
% 0.18/0.44      inference(monotonicity,[status(thm)],[67])).
% 0.18/0.44  tff(69,plain,
% 0.18/0.44      (s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))) = s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))),
% 0.18/0.44      inference(monotonicity,[status(thm)],[68])).
% 0.18/0.44  tff(70,plain,
% 0.18/0.44      (s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))) = s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)),
% 0.18/0.44      inference(transitivity,[status(thm)],[69, 57])).
% 0.18/0.44  tff(71,plain,
% 0.18/0.44      (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) <=> p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))),
% 0.18/0.44      inference(monotonicity,[status(thm)],[70])).
% 0.18/0.44  tff(72,plain,
% 0.18/0.44      (p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)) <=> p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))),
% 0.18/0.44      inference(symmetry,[status(thm)],[71])).
% 0.18/0.44  tff(73,plain,
% 0.18/0.44      (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))),
% 0.18/0.44      inference(modus_ponens,[status(thm)],[41, 72])).
% 0.18/0.44  tff(74,plain,
% 0.18/0.44      (^[A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : refl((p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))))),
% 0.18/0.44      inference(bind,[status(th)],[])).
% 0.18/0.44  tff(75,plain,
% 0.18/0.44      (![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))) <=> ![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))))),
% 0.18/0.44      inference(quant_intro,[status(thm)],[74])).
% 0.18/0.44  tff(76,plain,
% 0.18/0.44      (^[A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : rewrite((p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))))),
% 0.18/0.44      inference(bind,[status(th)],[])).
% 0.18/0.44  tff(77,plain,
% 0.18/0.44      (![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))) <=> ![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))))),
% 0.18/0.44      inference(quant_intro,[status(thm)],[76])).
% 0.18/0.44  tff(78,plain,
% 0.18/0.44      (![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))) <=> ![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))))),
% 0.18/0.44      inference(rewrite,[status(thm)],[])).
% 0.18/0.44  tff(79,axiom,(![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm_2Epred__set_2EIN__DELETE')).
% 0.18/0.44  tff(80,plain,
% 0.18/0.44      (![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))))),
% 0.18/0.44      inference(modus_ponens,[status(thm)],[79, 78])).
% 0.18/0.44  tff(81,plain,(
% 0.18/0.44      ![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))))),
% 0.18/0.44      inference(skolemize,[status(sab)],[80])).
% 0.18/0.44  tff(82,plain,
% 0.18/0.44      (![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))))),
% 0.18/0.44      inference(modus_ponens,[status(thm)],[81, 77])).
% 0.18/0.44  tff(83,plain,
% 0.18/0.44      (![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))))),
% 0.18/0.44      inference(modus_ponens,[status(thm)],[82, 75])).
% 0.18/0.44  tff(84,plain,
% 0.18/0.44      ((~![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))))) | (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))),
% 0.18/0.44      inference(quant_inst,[status(thm)],[])).
% 0.18/0.44  tff(85,plain,
% 0.18/0.44      (p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))),
% 0.18/0.44      inference(unit_resolution,[status(thm)],[84, 83])).
% 0.18/0.44  tff(86,plain,
% 0.18/0.44      ((p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))),
% 0.18/0.44      inference(tautology,[status(thm)],[])).
% 0.18/0.44  tff(87,plain,
% 0.18/0.44      (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))),
% 0.18/0.45      inference(unit_resolution,[status(thm)],[86, 36])).
% 0.18/0.45  tff(88,plain,
% 0.18/0.45      (((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))),
% 0.18/0.45      inference(tautology,[status(thm)],[])).
% 0.18/0.45  tff(89,plain,
% 0.18/0.45      ((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))),
% 0.18/0.45      inference(unit_resolution,[status(thm)],[88, 87])).
% 0.18/0.45  tff(90,plain,
% 0.18/0.45      ((~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))) | (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))),
% 0.18/0.45      inference(tautology,[status(thm)],[])).
% 0.18/0.45  tff(91,plain,
% 0.18/0.45      ((~(p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) | (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))),
% 0.18/0.45      inference(unit_resolution,[status(thm)],[90, 89])).
% 0.18/0.45  tff(92,plain,
% 0.18/0.45      (~p(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))),
% 0.18/0.45      inference(unit_resolution,[status(thm)],[91, 85])).
% 0.18/0.45  tff(93,plain,
% 0.18/0.45      ($false),
% 0.18/0.45      inference(unit_resolution,[status(thm)],[92, 73])).
% 0.18/0.45  % SZS output end Proof
%------------------------------------------------------------------------------