TSTP Solution File: ITP004+2 by Z3---4.8.9.0

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ITP004+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n009.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 04:14:39 EDT 2022

% Result   : Theorem 1.54s 1.22s
% Output   : Proof 1.60s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : ITP004+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.03/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n009.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 01:50:50 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 1.54/1.22  % SZS status Theorem
% 1.54/1.22  % SZS output start Proof
% 1.54/1.22  tff(p_type, type, (
% 1.54/1.22     p: $i > $o)).
% 1.54/1.22  tff(ap_type, type, (
% 1.54/1.22     ap: ( $i * $i ) > $i)).
% 1.54/1.22  tff(tptp_fun_V0s_4_type, type, (
% 1.54/1.22     tptp_fun_V0s_4: $i)).
% 1.54/1.22  tff(c_2Epred__set_2ECHOICE_type, type, (
% 1.54/1.22     c_2Epred__set_2ECHOICE: $i > $i)).
% 1.54/1.22  tff(tptp_fun_A_27a_3_type, type, (
% 1.54/1.22     tptp_fun_A_27a_3: $i)).
% 1.54/1.22  tff(c_2Epred__set_2EDELETE_type, type, (
% 1.54/1.22     c_2Epred__set_2EDELETE: $i > $i)).
% 1.54/1.22  tff(tptp_fun_V2x_2_type, type, (
% 1.54/1.22     tptp_fun_V2x_2: ( $i * $i * $i ) > $i)).
% 1.54/1.22  tff(c_2Epred__set_2EREST_type, type, (
% 1.54/1.22     c_2Epred__set_2EREST: $i > $i)).
% 1.54/1.22  tff(c_2Ebool_2EIN_type, type, (
% 1.54/1.22     c_2Ebool_2EIN: $i > $i)).
% 1.54/1.22  tff(mem_type, type, (
% 1.54/1.22     mem: ( $i * $i ) > $o)).
% 1.54/1.22  tff(arr_type, type, (
% 1.54/1.22     arr: ( $i * $i ) > $i)).
% 1.54/1.22  tff(bool_type, type, (
% 1.54/1.22     bool: $i)).
% 1.54/1.22  tff(ne_type, type, (
% 1.54/1.22     ne: $i > $o)).
% 1.54/1.22  tff(c_2Epred__set_2ESUBSET_type, type, (
% 1.54/1.22     c_2Epred__set_2ESUBSET: $i > $i)).
% 1.54/1.22  tff(1,plain,
% 1.54/1.22      (((~(~ne(A_27a!3))) & (~((~mem(V0s!4, arr(A_27a!3, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))))) <=> (ne(A_27a!3) & (~((~mem(V0s!4, arr(A_27a!3, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)))))),
% 1.54/1.22      inference(rewrite,[status(thm)],[])).
% 1.54/1.22  tff(2,plain,
% 1.54/1.22      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))) <=> (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))))),
% 1.54/1.22      inference(rewrite,[status(thm)],[])).
% 1.54/1.22  tff(3,plain,
% 1.54/1.22      ((~![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))) <=> (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))))),
% 1.54/1.22      inference(rewrite,[status(thm)],[])).
% 1.54/1.22  tff(4,axiom,(~![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_thm_2Epred__set_2EREST__SUBSET')).
% 1.54/1.22  tff(5,plain,
% 1.54/1.22      (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[4, 3])).
% 1.54/1.22  tff(6,plain,
% 1.54/1.22      (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[5, 2])).
% 1.54/1.22  tff(7,plain,
% 1.54/1.22      (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[6, 2])).
% 1.54/1.22  tff(8,plain,
% 1.54/1.22      (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[7, 2])).
% 1.54/1.22  tff(9,plain,
% 1.54/1.22      (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[8, 2])).
% 1.54/1.22  tff(10,plain,
% 1.54/1.22      (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[9, 2])).
% 1.54/1.22  tff(11,plain,
% 1.54/1.22      (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[10, 2])).
% 1.54/1.22  tff(12,plain,
% 1.54/1.22      (ne(A_27a!3) & (~((~mem(V0s!4, arr(A_27a!3, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[11, 1])).
% 1.54/1.22  tff(13,plain,
% 1.54/1.22      (ne(A_27a!3)),
% 1.54/1.22      inference(and_elim,[status(thm)],[12])).
% 1.54/1.22  tff(14,plain,
% 1.54/1.22      (^[A_27a: $i] : refl(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))))),
% 1.54/1.22      inference(bind,[status(th)],[])).
% 1.54/1.22  tff(15,plain,
% 1.54/1.22      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.54/1.22      inference(quant_intro,[status(thm)],[14])).
% 1.54/1.22  tff(16,plain,
% 1.54/1.22      (^[A_27a: $i] : rewrite(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))))),
% 1.54/1.22      inference(bind,[status(th)],[])).
% 1.54/1.22  tff(17,plain,
% 1.54/1.22      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.54/1.22      inference(quant_intro,[status(thm)],[16])).
% 1.54/1.22  tff(18,plain,
% 1.54/1.22      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.54/1.22      inference(transitivity,[status(thm)],[17, 15])).
% 1.54/1.22  tff(19,plain,
% 1.54/1.22      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.54/1.22      inference(rewrite,[status(thm)],[])).
% 1.54/1.22  tff(20,plain,
% 1.54/1.22      (^[A_27a: $i] : trans(monotonicity(quant_intro(proof_bind(^[V0s: $i] : rewrite((mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))) <=> ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))), (![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))) <=> ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))), ((ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> (ne(A_27a) => ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))))), rewrite((ne(A_27a) => ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))), ((ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))))),
% 1.54/1.22      inference(bind,[status(th)],[])).
% 1.54/1.22  tff(21,plain,
% 1.54/1.22      (![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.54/1.22      inference(quant_intro,[status(thm)],[20])).
% 1.54/1.22  tff(22,axiom,(![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax_thm_2Epred__set_2EREST__DEF')).
% 1.54/1.22  tff(23,plain,
% 1.54/1.22      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[22, 21])).
% 1.54/1.22  tff(24,plain,
% 1.54/1.22      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[23, 19])).
% 1.54/1.22  tff(25,plain,(
% 1.54/1.22      ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.54/1.22      inference(skolemize,[status(sab)],[24])).
% 1.54/1.22  tff(26,plain,
% 1.54/1.22      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[25, 18])).
% 1.54/1.22  tff(27,plain,
% 1.54/1.22      (((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s)))))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s)))))),
% 1.54/1.22      inference(rewrite,[status(thm)],[])).
% 1.54/1.22  tff(28,plain,
% 1.54/1.22      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s)))))),
% 1.54/1.22      inference(quant_inst,[status(thm)],[])).
% 1.54/1.22  tff(29,plain,
% 1.54/1.22      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[28, 27])).
% 1.54/1.22  tff(30,plain,
% 1.54/1.22      (![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s))))),
% 1.54/1.22      inference(unit_resolution,[status(thm)],[29, 26, 13])).
% 1.54/1.22  tff(31,plain,
% 1.54/1.22      (~((~mem(V0s!4, arr(A_27a!3, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)))),
% 1.54/1.22      inference(and_elim,[status(thm)],[12])).
% 1.54/1.22  tff(32,plain,
% 1.54/1.22      (mem(V0s!4, arr(A_27a!3, bool))),
% 1.54/1.22      inference(or_elim,[status(thm)],[31])).
% 1.54/1.22  tff(33,plain,
% 1.54/1.22      (((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s!4) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))) <=> ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s))))) | (~mem(V0s!4, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s!4) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))),
% 1.54/1.22      inference(rewrite,[status(thm)],[])).
% 1.54/1.22  tff(34,plain,
% 1.54/1.22      ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s!4) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))),
% 1.54/1.22      inference(quant_inst,[status(thm)],[])).
% 1.54/1.22  tff(35,plain,
% 1.54/1.22      ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s))))) | (~mem(V0s!4, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s!4) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[34, 33])).
% 1.54/1.22  tff(36,plain,
% 1.54/1.22      (ap(c_2Epred__set_2EREST(A_27a!3), V0s!4) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))),
% 1.54/1.22      inference(unit_resolution,[status(thm)],[35, 32, 30])).
% 1.54/1.22  tff(37,plain,
% 1.54/1.22      (ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)) = ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)),
% 1.54/1.22      inference(symmetry,[status(thm)],[36])).
% 1.54/1.22  tff(38,plain,
% 1.54/1.22      (ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))) = ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))),
% 1.54/1.22      inference(monotonicity,[status(thm)],[37])).
% 1.54/1.22  tff(39,plain,
% 1.54/1.22      (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))),
% 1.54/1.22      inference(monotonicity,[status(thm)],[38])).
% 1.54/1.22  tff(40,plain,
% 1.54/1.22      (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))),
% 1.54/1.22      inference(symmetry,[status(thm)],[39])).
% 1.54/1.22  tff(41,plain,
% 1.54/1.22      (^[A_27a: $i] : refl(((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))) <=> ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))))),
% 1.54/1.22      inference(bind,[status(th)],[])).
% 1.54/1.22  tff(42,plain,
% 1.54/1.22      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))) <=> ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.54/1.22      inference(quant_intro,[status(thm)],[41])).
% 1.54/1.22  tff(43,plain,
% 1.54/1.22      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))) <=> ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.54/1.22      inference(rewrite,[status(thm)],[])).
% 1.54/1.22  tff(44,plain,
% 1.54/1.22      (^[A_27a: $i] : rewrite((ne(A_27a) => mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))) <=> ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))))),
% 1.54/1.22      inference(bind,[status(th)],[])).
% 1.54/1.22  tff(45,plain,
% 1.54/1.22      (![A_27a: $i] : (ne(A_27a) => mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))) <=> ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.54/1.22      inference(quant_intro,[status(thm)],[44])).
% 1.54/1.22  tff(46,axiom,(![A_27a: $i] : (ne(A_27a) => mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mem_c_2Epred__set_2EREST')).
% 1.54/1.22  tff(47,plain,
% 1.54/1.22      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[46, 45])).
% 1.54/1.22  tff(48,plain,
% 1.54/1.22      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[47, 43])).
% 1.54/1.22  tff(49,plain,(
% 1.54/1.22      ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.54/1.22      inference(skolemize,[status(sab)],[48])).
% 1.54/1.22  tff(50,plain,
% 1.54/1.22      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[49, 42])).
% 1.54/1.22  tff(51,plain,
% 1.54/1.22      (((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))) | ((~ne(A_27a!3)) | mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool))))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))) | (~ne(A_27a!3)) | mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool))))),
% 1.54/1.22      inference(rewrite,[status(thm)],[])).
% 1.54/1.22  tff(52,plain,
% 1.54/1.22      ((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))) | ((~ne(A_27a!3)) | mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool))))),
% 1.54/1.22      inference(quant_inst,[status(thm)],[])).
% 1.54/1.22  tff(53,plain,
% 1.54/1.22      ((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))) | (~ne(A_27a!3)) | mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool)))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[52, 51])).
% 1.54/1.22  tff(54,plain,
% 1.54/1.22      (mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool)))),
% 1.54/1.22      inference(unit_resolution,[status(thm)],[53, 50, 13])).
% 1.54/1.22  tff(55,plain,
% 1.54/1.22      (^[A: $i, B: $i, F: $i] : refl(((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))),
% 1.54/1.22      inference(bind,[status(th)],[])).
% 1.54/1.22  tff(56,plain,
% 1.54/1.22      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.54/1.22      inference(quant_intro,[status(thm)],[55])).
% 1.54/1.22  tff(57,plain,
% 1.54/1.22      (^[A: $i, B: $i, F: $i] : rewrite(((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))),
% 1.54/1.22      inference(bind,[status(th)],[])).
% 1.54/1.22  tff(58,plain,
% 1.54/1.22      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.54/1.22      inference(quant_intro,[status(thm)],[57])).
% 1.54/1.22  tff(59,plain,
% 1.54/1.22      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.54/1.22      inference(transitivity,[status(thm)],[58, 56])).
% 1.54/1.22  tff(60,plain,
% 1.54/1.22      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.54/1.22      inference(rewrite,[status(thm)],[])).
% 1.54/1.22  tff(61,plain,
% 1.54/1.22      (^[A: $i, B: $i, F: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite((mem(X, A) => mem(ap(F, X), B)) <=> ((~mem(X, A)) | mem(ap(F, X), B)))), (![X: $i] : (mem(X, A) => mem(ap(F, X), B)) <=> ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))), ((mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> (mem(F, arr(A, B)) => ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))), rewrite((mem(F, arr(A, B)) => ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))), ((mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))))),
% 1.54/1.22      inference(bind,[status(th)],[])).
% 1.54/1.22  tff(62,plain,
% 1.54/1.22      (![A: $i, B: $i, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> ![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.54/1.22      inference(quant_intro,[status(thm)],[61])).
% 1.54/1.22  tff(63,axiom,(![A: $i, B: $i, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B)))), file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax','ap_tp')).
% 1.54/1.22  tff(64,plain,
% 1.54/1.22      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[63, 62])).
% 1.54/1.22  tff(65,plain,
% 1.54/1.22      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[64, 60])).
% 1.54/1.22  tff(66,plain,(
% 1.54/1.22      ![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.54/1.22      inference(skolemize,[status(sab)],[65])).
% 1.54/1.22  tff(67,plain,
% 1.54/1.22      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[66, 59])).
% 1.54/1.22  tff(68,plain,
% 1.54/1.22      (((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool))))) <=> ((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool))))),
% 1.54/1.22      inference(rewrite,[status(thm)],[])).
% 1.54/1.22  tff(69,plain,
% 1.54/1.22      ((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool))))),
% 1.54/1.22      inference(quant_inst,[status(thm)],[])).
% 1.54/1.22  tff(70,plain,
% 1.54/1.22      ((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool)))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[69, 68])).
% 1.54/1.22  tff(71,plain,
% 1.54/1.22      (![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool)))),
% 1.54/1.22      inference(unit_resolution,[status(thm)],[70, 67, 54])).
% 1.54/1.22  tff(72,plain,
% 1.54/1.22      (((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool)))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool)))) <=> ((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool)))) | (~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool)))),
% 1.54/1.22      inference(rewrite,[status(thm)],[])).
% 1.54/1.22  tff(73,plain,
% 1.54/1.22      ((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool)))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool)))),
% 1.54/1.22      inference(quant_inst,[status(thm)],[])).
% 1.54/1.22  tff(74,plain,
% 1.54/1.22      ((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool)))) | (~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))),
% 1.54/1.22      inference(modus_ponens,[status(thm)],[73, 72])).
% 1.54/1.22  tff(75,plain,
% 1.54/1.22      (mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))),
% 1.54/1.22      inference(unit_resolution,[status(thm)],[74, 32, 71])).
% 1.54/1.22  tff(76,plain,
% 1.54/1.22      (^[A_27a: $i] : rewrite(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))))),
% 1.54/1.22      inference(bind,[status(th)],[])).
% 1.54/1.22  tff(77,plain,
% 1.54/1.22      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))),
% 1.54/1.23      inference(quant_intro,[status(thm)],[76])).
% 1.54/1.23  tff(78,plain,
% 1.54/1.23      (^[A_27a: $i] : refl(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))))),
% 1.54/1.23      inference(bind,[status(th)],[])).
% 1.54/1.23  tff(79,plain,
% 1.54/1.23      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 1.54/1.23      inference(quant_intro,[status(thm)],[78])).
% 1.54/1.23  tff(80,plain,
% 1.54/1.23      (^[A_27a: $i] : rewrite(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))))),
% 1.54/1.23      inference(bind,[status(th)],[])).
% 1.54/1.23  tff(81,plain,
% 1.54/1.23      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 1.54/1.23      inference(quant_intro,[status(thm)],[80])).
% 1.54/1.23  tff(82,plain,
% 1.54/1.23      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 1.54/1.23      inference(transitivity,[status(thm)],[81, 79])).
% 1.54/1.23  tff(83,plain,
% 1.54/1.23      (^[A_27a: $i] : rewrite(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))) & (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))))),
% 1.54/1.23      inference(bind,[status(th)],[])).
% 1.54/1.23  tff(84,plain,
% 1.54/1.23      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))) & (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 1.54/1.23      inference(quant_intro,[status(thm)],[83])).
% 1.54/1.23  tff(85,plain,
% 1.54/1.23      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))),
% 1.54/1.23      inference(rewrite,[status(thm)],[])).
% 1.54/1.23  tff(86,plain,
% 1.54/1.23      (^[A_27a: $i] : trans(monotonicity(quant_intro(proof_bind(^[V0s: $i] : trans(monotonicity(quant_intro(proof_bind(^[V1t: $i] : trans(monotonicity(rewrite((p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))) <=> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))), ((mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))) <=> (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))), rewrite((mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) <=> ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))), ((mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))) <=> ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))), (![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))) <=> ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))), ((mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))))) <=> (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))), rewrite((mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))), ((mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))), (![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))))) <=> ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))), ((ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))))) <=> (ne(A_27a) => ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))), rewrite((ne(A_27a) => ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))), ((ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))),
% 1.59/1.23      inference(bind,[status(th)],[])).
% 1.59/1.23  tff(87,plain,
% 1.59/1.23      (![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))),
% 1.59/1.23      inference(quant_intro,[status(thm)],[86])).
% 1.59/1.23  tff(88,axiom,(![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax_thm_2Epred__set_2ESUBSET__DEF')).
% 1.59/1.23  tff(89,plain,
% 1.59/1.23      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))),
% 1.59/1.23      inference(modus_ponens,[status(thm)],[88, 87])).
% 1.59/1.23  tff(90,plain,
% 1.59/1.23      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))),
% 1.59/1.23      inference(modus_ponens,[status(thm)],[89, 85])).
% 1.59/1.23  tff(91,plain,(
% 1.59/1.23      ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))) & (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))),
% 1.59/1.23      inference(skolemize,[status(sab)],[90])).
% 1.59/1.23  tff(92,plain,
% 1.59/1.23      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 1.59/1.23      inference(modus_ponens,[status(thm)],[91, 84])).
% 1.59/1.23  tff(93,plain,
% 1.59/1.23      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 1.59/1.23      inference(modus_ponens,[status(thm)],[92, 82])).
% 1.59/1.23  tff(94,plain,
% 1.59/1.23      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))),
% 1.59/1.23      inference(modus_ponens,[status(thm)],[93, 77])).
% 1.59/1.23  tff(95,plain,
% 1.59/1.23      (((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))),
% 1.59/1.23      inference(rewrite,[status(thm)],[])).
% 1.59/1.23  tff(96,plain,
% 1.59/1.23      (((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~mem(V2x, A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) <=> ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))),
% 1.59/1.23      inference(rewrite,[status(thm)],[])).
% 1.59/1.23  tff(97,plain,
% 1.59/1.23      (((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~mem(V2x, A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))))),
% 1.59/1.23      inference(monotonicity,[status(thm)],[96])).
% 1.59/1.23  tff(98,plain,
% 1.59/1.23      (((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~mem(V2x, A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))),
% 1.59/1.23      inference(transitivity,[status(thm)],[97, 95])).
% 1.59/1.23  tff(99,plain,
% 1.59/1.23      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~mem(V2x, A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))),
% 1.59/1.23      inference(quant_inst,[status(thm)],[])).
% 1.59/1.23  tff(100,plain,
% 1.59/1.23      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))),
% 1.59/1.23      inference(modus_ponens,[status(thm)],[99, 98])).
% 1.59/1.23  tff(101,plain,
% 1.59/1.23      (![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))),
% 1.59/1.23      inference(unit_resolution,[status(thm)],[100, 94, 13])).
% 1.59/1.23  tff(102,plain,
% 1.59/1.23      (((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))) <=> ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) | (~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))),
% 1.60/1.23      inference(rewrite,[status(thm)],[])).
% 1.60/1.23  tff(103,plain,
% 1.60/1.23      ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))),
% 1.60/1.23      inference(quant_inst,[status(thm)],[])).
% 1.60/1.23  tff(104,plain,
% 1.60/1.23      ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) | (~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))),
% 1.60/1.24      inference(modus_ponens,[status(thm)],[103, 102])).
% 1.60/1.24  tff(105,plain,
% 1.60/1.24      ((~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))),
% 1.60/1.24      inference(unit_resolution,[status(thm)],[104, 101])).
% 1.60/1.24  tff(106,plain,
% 1.60/1.24      (![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))),
% 1.60/1.24      inference(unit_resolution,[status(thm)],[105, 75])).
% 1.60/1.24  tff(107,plain,
% 1.60/1.24      (((~![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))) <=> ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))) | (~mem(V0s!4, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))),
% 1.60/1.24      inference(rewrite,[status(thm)],[])).
% 1.60/1.24  tff(108,plain,
% 1.60/1.24      ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))),
% 1.60/1.24      inference(quant_inst,[status(thm)],[])).
% 1.60/1.24  tff(109,plain,
% 1.60/1.24      ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))) | (~mem(V0s!4, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))),
% 1.60/1.24      inference(modus_ponens,[status(thm)],[108, 107])).
% 1.60/1.24  tff(110,plain,
% 1.60/1.24      (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))),
% 1.60/1.24      inference(unit_resolution,[status(thm)],[109, 32, 106])).
% 1.60/1.24  tff(111,plain,
% 1.60/1.24      (((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))),
% 1.60/1.24      inference(tautology,[status(thm)],[])).
% 1.60/1.24  tff(112,plain,
% 1.60/1.24      (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))),
% 1.60/1.24      inference(unit_resolution,[status(thm)],[111, 110])).
% 1.60/1.24  tff(113,plain,
% 1.60/1.24      (~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))),
% 1.60/1.24      inference(or_elim,[status(thm)],[31])).
% 1.60/1.24  tff(114,plain,
% 1.60/1.24      ((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))),
% 1.60/1.24      inference(tautology,[status(thm)],[])).
% 1.60/1.24  tff(115,plain,
% 1.60/1.24      ((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))),
% 1.60/1.24      inference(unit_resolution,[status(thm)],[114, 113])).
% 1.60/1.24  tff(116,plain,
% 1.60/1.24      (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))),
% 1.60/1.24      inference(unit_resolution,[status(thm)],[115, 112])).
% 1.60/1.24  tff(117,plain,
% 1.60/1.24      ((p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))),
% 1.60/1.24      inference(tautology,[status(thm)],[])).
% 1.60/1.24  tff(118,plain,
% 1.60/1.24      (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))),
% 1.60/1.24      inference(unit_resolution,[status(thm)],[117, 116])).
% 1.60/1.24  tff(119,plain,
% 1.60/1.24      (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))),
% 1.60/1.24      inference(modus_ponens,[status(thm)],[118, 40])).
% 1.60/1.24  tff(120,plain,
% 1.60/1.24      ((p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))) | mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)),
% 1.60/1.24      inference(tautology,[status(thm)],[])).
% 1.60/1.24  tff(121,plain,
% 1.60/1.24      (mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)),
% 1.60/1.24      inference(unit_resolution,[status(thm)],[120, 116])).
% 1.60/1.24  tff(122,plain,
% 1.60/1.24      (^[A_27a: $i] : refl(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))))),
% 1.60/1.24      inference(bind,[status(th)],[])).
% 1.60/1.24  tff(123,plain,
% 1.60/1.24      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))))),
% 1.60/1.24      inference(quant_intro,[status(thm)],[122])).
% 1.60/1.24  tff(124,plain,
% 1.60/1.24      (^[A_27a: $i] : rewrite(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))))),
% 1.60/1.24      inference(bind,[status(th)],[])).
% 1.60/1.24  tff(125,plain,
% 1.60/1.24      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))))),
% 1.60/1.24      inference(quant_intro,[status(thm)],[124])).
% 1.60/1.24  tff(126,plain,
% 1.60/1.24      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))))),
% 1.60/1.24      inference(transitivity,[status(thm)],[125, 123])).
% 1.60/1.24  tff(127,plain,
% 1.60/1.24      (^[A_27a: $i] : rewrite(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))))),
% 1.60/1.24      inference(bind,[status(th)],[])).
% 1.60/1.24  tff(128,plain,
% 1.60/1.24      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))))),
% 1.60/1.24      inference(quant_intro,[status(thm)],[127])).
% 1.60/1.24  tff(129,plain,
% 1.60/1.24      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))),
% 1.60/1.24      inference(rewrite,[status(thm)],[])).
% 1.60/1.24  tff(130,plain,
% 1.60/1.24      (^[A_27a: $i] : trans(monotonicity(quant_intro(proof_bind(^[V0s: $i] : trans(monotonicity(quant_intro(proof_bind(^[V1x: $i] : trans(monotonicity(quant_intro(proof_bind(^[V2y: $i] : rewrite((mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))) <=> ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))), (![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))) <=> ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))), ((mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))) <=> (mem(V1x, A_27a) => ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))), rewrite((mem(V1x, A_27a) => ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))) <=> ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))), ((mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))) <=> ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))), (![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))) <=> ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))), ((mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))), rewrite((mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))), ((mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))))), (![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))), ((ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> (ne(A_27a) => ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))))), rewrite((ne(A_27a) => ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))), ((ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))))),
% 1.60/1.24      inference(bind,[status(th)],[])).
% 1.60/1.24  tff(131,plain,
% 1.60/1.24      (![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))),
% 1.60/1.24      inference(quant_intro,[status(thm)],[130])).
% 1.60/1.24  tff(132,axiom,(![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_thm_2Epred__set_2EIN__DELETE')).
% 1.60/1.24  tff(133,plain,
% 1.60/1.24      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))),
% 1.60/1.24      inference(modus_ponens,[status(thm)],[132, 131])).
% 1.60/1.24  tff(134,plain,
% 1.60/1.24      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))),
% 1.60/1.24      inference(modus_ponens,[status(thm)],[133, 129])).
% 1.60/1.24  tff(135,plain,(
% 1.60/1.24      ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))),
% 1.60/1.24      inference(skolemize,[status(sab)],[134])).
% 1.60/1.24  tff(136,plain,
% 1.60/1.24      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))))),
% 1.60/1.24      inference(modus_ponens,[status(thm)],[135, 128])).
% 1.60/1.24  tff(137,plain,
% 1.60/1.24      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))))),
% 1.60/1.24      inference(modus_ponens,[status(thm)],[136, 126])).
% 1.60/1.24  tff(138,plain,
% 1.60/1.24      (((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y))))))))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y))))))))),
% 1.60/1.24      inference(rewrite,[status(thm)],[])).
% 1.60/1.24  tff(139,plain,
% 1.60/1.24      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y))))))))),
% 1.60/1.25      inference(quant_inst,[status(thm)],[])).
% 1.60/1.25  tff(140,plain,
% 1.60/1.25      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)))))))),
% 1.60/1.25      inference(modus_ponens,[status(thm)],[139, 138])).
% 1.60/1.25  tff(141,plain,
% 1.60/1.25      (![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)))))))),
% 1.60/1.25      inference(unit_resolution,[status(thm)],[140, 137, 13])).
% 1.60/1.25  tff(142,plain,
% 1.60/1.25      (((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)))))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y)))))))) <=> ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)))))))) | (~mem(V0s!4, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y)))))))),
% 1.60/1.25      inference(rewrite,[status(thm)],[])).
% 1.60/1.25  tff(143,plain,
% 1.60/1.25      ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)))))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y)))))))),
% 1.60/1.25      inference(quant_inst,[status(thm)],[])).
% 1.60/1.25  tff(144,plain,
% 1.60/1.25      ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)))))))) | (~mem(V0s!4, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y))))))),
% 1.60/1.25      inference(modus_ponens,[status(thm)],[143, 142])).
% 1.60/1.25  tff(145,plain,
% 1.60/1.25      (![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y))))))),
% 1.60/1.25      inference(unit_resolution,[status(thm)],[144, 32, 141])).
% 1.60/1.25  tff(146,plain,
% 1.60/1.25      (((~![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y))))))) | ((~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y))))))) <=> ((~![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y))))))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y))))))),
% 1.60/1.25      inference(rewrite,[status(thm)],[])).
% 1.60/1.25  tff(147,plain,
% 1.60/1.25      ((~![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y))))))) | ((~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y))))))),
% 1.60/1.25      inference(quant_inst,[status(thm)],[])).
% 1.60/1.25  tff(148,plain,
% 1.60/1.25      ((~![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y))))))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)))))),
% 1.60/1.25      inference(modus_ponens,[status(thm)],[147, 146])).
% 1.60/1.25  tff(149,plain,
% 1.60/1.25      (![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)))))),
% 1.60/1.25      inference(unit_resolution,[status(thm)],[148, 145, 121])).
% 1.60/1.25  tff(150,plain,
% 1.60/1.25      (^[A_27a: $i] : refl(((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))) <=> ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))))),
% 1.60/1.25      inference(bind,[status(th)],[])).
% 1.60/1.25  tff(151,plain,
% 1.60/1.25      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))) <=> ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.60/1.25      inference(quant_intro,[status(thm)],[150])).
% 1.60/1.25  tff(152,plain,
% 1.60/1.25      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))) <=> ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.60/1.25      inference(rewrite,[status(thm)],[])).
% 1.60/1.25  tff(153,plain,
% 1.60/1.25      (^[A_27a: $i] : rewrite((ne(A_27a) => mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))) <=> ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))))),
% 1.60/1.25      inference(bind,[status(th)],[])).
% 1.60/1.25  tff(154,plain,
% 1.60/1.25      (![A_27a: $i] : (ne(A_27a) => mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))) <=> ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.60/1.25      inference(quant_intro,[status(thm)],[153])).
% 1.60/1.25  tff(155,axiom,(![A_27a: $i] : (ne(A_27a) => mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mem_c_2Epred__set_2ECHOICE')).
% 1.60/1.25  tff(156,plain,
% 1.60/1.25      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.60/1.25      inference(modus_ponens,[status(thm)],[155, 154])).
% 1.60/1.25  tff(157,plain,
% 1.60/1.25      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.60/1.25      inference(modus_ponens,[status(thm)],[156, 152])).
% 1.60/1.25  tff(158,plain,(
% 1.60/1.25      ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.60/1.25      inference(skolemize,[status(sab)],[157])).
% 1.60/1.25  tff(159,plain,
% 1.60/1.25      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.60/1.25      inference(modus_ponens,[status(thm)],[158, 151])).
% 1.60/1.25  tff(160,plain,
% 1.60/1.25      (((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))) | ((~ne(A_27a!3)) | mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3)))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))) | (~ne(A_27a!3)) | mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3)))),
% 1.60/1.25      inference(rewrite,[status(thm)],[])).
% 1.60/1.25  tff(161,plain,
% 1.60/1.25      ((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))) | ((~ne(A_27a!3)) | mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3)))),
% 1.60/1.25      inference(quant_inst,[status(thm)],[])).
% 1.60/1.25  tff(162,plain,
% 1.60/1.25      ((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))) | (~ne(A_27a!3)) | mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3))),
% 1.60/1.25      inference(modus_ponens,[status(thm)],[161, 160])).
% 1.60/1.25  tff(163,plain,
% 1.60/1.25      (mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3))),
% 1.60/1.25      inference(unit_resolution,[status(thm)],[162, 159, 13])).
% 1.60/1.25  tff(164,plain,
% 1.60/1.25      (((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3)))) <=> ((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3)))),
% 1.60/1.25      inference(rewrite,[status(thm)],[])).
% 1.60/1.25  tff(165,plain,
% 1.60/1.25      ((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3)))),
% 1.60/1.25      inference(quant_inst,[status(thm)],[])).
% 1.60/1.25  tff(166,plain,
% 1.60/1.25      ((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3))),
% 1.60/1.25      inference(modus_ponens,[status(thm)],[165, 164])).
% 1.60/1.25  tff(167,plain,
% 1.60/1.25      (![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3))),
% 1.60/1.25      inference(unit_resolution,[status(thm)],[166, 67, 163])).
% 1.60/1.25  tff(168,plain,
% 1.60/1.25      (((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3))) <=> ((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3))) | (~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3))),
% 1.60/1.25      inference(rewrite,[status(thm)],[])).
% 1.60/1.25  tff(169,plain,
% 1.60/1.25      ((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3))),
% 1.60/1.25      inference(quant_inst,[status(thm)],[])).
% 1.60/1.25  tff(170,plain,
% 1.60/1.25      ((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3))) | (~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3)),
% 1.60/1.25      inference(modus_ponens,[status(thm)],[169, 168])).
% 1.60/1.25  tff(171,plain,
% 1.60/1.25      (mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3)),
% 1.60/1.25      inference(unit_resolution,[status(thm)],[170, 32, 167])).
% 1.60/1.25  tff(172,plain,
% 1.60/1.25      (((~![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)))))) | ((~mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))))) <=> ((~![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)))))) | (~mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))))),
% 1.60/1.25      inference(rewrite,[status(thm)],[])).
% 1.60/1.25  tff(173,plain,
% 1.60/1.25      ((~![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)))))) | ((~mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))))),
% 1.60/1.25      inference(quant_inst,[status(thm)],[])).
% 1.60/1.25  tff(174,plain,
% 1.60/1.25      ((~![V2y: $i] : ((~mem(V2y, A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)))))) | (~mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))))),
% 1.60/1.25      inference(modus_ponens,[status(thm)],[173, 172])).
% 1.60/1.25  tff(175,plain,
% 1.60/1.25      (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))),
% 1.60/1.25      inference(unit_resolution,[status(thm)],[174, 171, 149])).
% 1.60/1.25  tff(176,plain,
% 1.60/1.25      ((p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)))),
% 1.60/1.25      inference(tautology,[status(thm)],[])).
% 1.60/1.25  tff(177,plain,
% 1.60/1.25      (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))),
% 1.60/1.25      inference(unit_resolution,[status(thm)],[176, 116])).
% 1.60/1.25  tff(178,plain,
% 1.60/1.25      (((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))),
% 1.60/1.25      inference(tautology,[status(thm)],[])).
% 1.60/1.25  tff(179,plain,
% 1.60/1.25      ((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))),
% 1.60/1.25      inference(unit_resolution,[status(thm)],[178, 177])).
% 1.60/1.25  tff(180,plain,
% 1.60/1.25      ((~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))))) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))),
% 1.60/1.26      inference(tautology,[status(thm)],[])).
% 1.60/1.26  tff(181,plain,
% 1.60/1.26      ((~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))))) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))))),
% 1.60/1.26      inference(unit_resolution,[status(thm)],[180, 179])).
% 1.60/1.26  tff(182,plain,
% 1.60/1.26      (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))),
% 1.60/1.26      inference(unit_resolution,[status(thm)],[181, 175])).
% 1.60/1.26  tff(183,plain,
% 1.60/1.26      ($false),
% 1.60/1.26      inference(unit_resolution,[status(thm)],[182, 119])).
% 1.60/1.26  % SZS output end Proof
%------------------------------------------------------------------------------