Z3---4.15.1.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : ITP004_2 : TPTP v9.0.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 05:11:15 AM UTC 2025

% Result   : Theorem 1.69s 1.86s
% Output   : Proof 1.69s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : ITP004_2 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Jun 19 18:04:33 EDT 2025
% 0.13/0.35  % CPUTime    : 
% 1.69/1.86  % SZS status Theorem
% 1.69/1.86  % SZS output start Proof
% 1.69/1.86  tff(p_type, type, (
% 1.69/1.86     p: $i > $o)).
% 1.69/1.86  tff(ap_type, type, (
% 1.69/1.86     ap: ( $i * $i ) > $i)).
% 1.69/1.86  tff(tptp_fun_V0s_3_type, type, (
% 1.69/1.86     tptp_fun_V0s_3: $i)).
% 1.69/1.86  tff(c_2Epred__set_2ECHOICE_type, type, (
% 1.69/1.86     c_2Epred__set_2ECHOICE: del > $i)).
% 1.69/1.86  tff(tptp_fun_A_27a_4_type, type, (
% 1.69/1.86     tptp_fun_A_27a_4: del)).
% 1.69/1.86  tff(c_2Epred__set_2EDELETE_type, type, (
% 1.69/1.86     c_2Epred__set_2EDELETE: del > $i)).
% 1.69/1.86  tff(tptp_fun_V2x_2_type, type, (
% 1.69/1.86     tptp_fun_V2x_2: ( $i * $i * del ) > $i)).
% 1.69/1.86  tff(c_2Epred__set_2EREST_type, type, (
% 1.69/1.86     c_2Epred__set_2EREST: del > $i)).
% 1.69/1.86  tff(c_2Ebool_2EIN_type, type, (
% 1.69/1.86     c_2Ebool_2EIN: del > $i)).
% 1.69/1.86  tff(mem_type, type, (
% 1.69/1.86     mem: ( $i * del ) > $o)).
% 1.69/1.86  tff(arr_type, type, (
% 1.69/1.86     arr: ( del * del ) > del)).
% 1.69/1.86  tff(bool_type, type, (
% 1.69/1.86     bool: del)).
% 1.69/1.86  tff(c_2Epred__set_2ESUBSET_type, type, (
% 1.69/1.86     c_2Epred__set_2ESUBSET: del > $i)).
% 1.69/1.86  tff(1,plain,
% 1.69/1.86      ((~![A_27a: del, 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: del, 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))))),
% 1.69/1.86      inference(rewrite,[status(thm)],[])).
% 1.69/1.86  tff(2,plain,
% 1.69/1.86      ((~![A_27a: del, 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: del, 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))))),
% 1.69/1.86      inference(rewrite,[status(thm)],[])).
% 1.69/1.86  tff(3,axiom,(~![A_27a: del, 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/sandbox2/benchmark/theBenchmark.p','conj_thm_2Epred__set_2EREST__SUBSET')).
% 1.69/1.86  tff(4,plain,
% 1.69/1.86      (~![A_27a: del, 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)))),
% 1.69/1.86      inference(modus_ponens,[status(thm)],[3, 2])).
% 1.69/1.86  tff(5,plain,
% 1.69/1.86      (~![A_27a: del, 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)))),
% 1.69/1.86      inference(modus_ponens,[status(thm)],[4, 1])).
% 1.69/1.86  tff(6,plain,
% 1.69/1.86      (~![A_27a: del, 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)))),
% 1.69/1.86      inference(modus_ponens,[status(thm)],[5, 1])).
% 1.69/1.86  tff(7,plain,
% 1.69/1.86      (~![A_27a: del, 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)))),
% 1.69/1.86      inference(modus_ponens,[status(thm)],[6, 1])).
% 1.69/1.86  tff(8,plain,(
% 1.69/1.86      ~((~mem(V0s!3, arr(A_27a!4, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)))),
% 1.69/1.86      inference(skolemize,[status(sab)],[7])).
% 1.69/1.86  tff(9,plain,
% 1.69/1.86      (mem(V0s!3, arr(A_27a!4, bool))),
% 1.69/1.86      inference(or_elim,[status(thm)],[8])).
% 1.69/1.86  tff(10,plain,
% 1.69/1.86      (^[A_27a: del, V0s: $i] : refl(((~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)))))),
% 1.69/1.86      inference(bind,[status(th)],[])).
% 1.69/1.86  tff(11,plain,
% 1.69/1.86      (![A_27a: del, 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: del, 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))))),
% 1.69/1.86      inference(quant_intro,[status(thm)],[10])).
% 1.69/1.86  tff(12,plain,
% 1.69/1.86      (![A_27a: del, 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: del, 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))))),
% 1.69/1.86      inference(rewrite,[status(thm)],[])).
% 1.69/1.86  tff(13,plain,
% 1.69/1.86      (^[A_27a: del, 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)))))),
% 1.69/1.86      inference(bind,[status(th)],[])).
% 1.69/1.86  tff(14,plain,
% 1.69/1.86      (![A_27a: del, 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: del, 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))))),
% 1.69/1.86      inference(quant_intro,[status(thm)],[13])).
% 1.69/1.86  tff(15,axiom,(![A_27a: del, 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/sandbox2/benchmark/theBenchmark.p','ax_thm_2Epred__set_2EREST__DEF')).
% 1.69/1.86  tff(16,plain,
% 1.69/1.86      (![A_27a: del, 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))))),
% 1.69/1.86      inference(modus_ponens,[status(thm)],[15, 14])).
% 1.69/1.86  tff(17,plain,
% 1.69/1.86      (![A_27a: del, 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))))),
% 1.69/1.86      inference(modus_ponens,[status(thm)],[16, 12])).
% 1.69/1.86  tff(18,plain,(
% 1.69/1.86      ![A_27a: del, 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))))),
% 1.69/1.86      inference(skolemize,[status(sab)],[17])).
% 1.69/1.86  tff(19,plain,
% 1.69/1.86      (![A_27a: del, 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))))),
% 1.69/1.86      inference(modus_ponens,[status(thm)],[18, 11])).
% 1.69/1.86  tff(20,plain,
% 1.69/1.86      (((~![A_27a: del, 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))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | (ap(c_2Epred__set_2EREST(A_27a!4), V0s!3) = ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))) <=> ((~![A_27a: del, 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))))) | (~mem(V0s!3, arr(A_27a!4, bool))) | (ap(c_2Epred__set_2EREST(A_27a!4), V0s!3) = ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))),
% 1.69/1.86      inference(rewrite,[status(thm)],[])).
% 1.69/1.86  tff(21,plain,
% 1.69/1.86      ((~![A_27a: del, 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))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | (ap(c_2Epred__set_2EREST(A_27a!4), V0s!3) = ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))),
% 1.69/1.86      inference(quant_inst,[status(thm)],[])).
% 1.69/1.86  tff(22,plain,
% 1.69/1.86      ((~![A_27a: del, 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))))) | (~mem(V0s!3, arr(A_27a!4, bool))) | (ap(c_2Epred__set_2EREST(A_27a!4), V0s!3) = ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))),
% 1.69/1.86      inference(modus_ponens,[status(thm)],[21, 20])).
% 1.69/1.86  tff(23,plain,
% 1.69/1.86      (ap(c_2Epred__set_2EREST(A_27a!4), V0s!3) = ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))),
% 1.69/1.87      inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 1.69/1.87  tff(24,plain,
% 1.69/1.87      (ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)) = ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)),
% 1.69/1.87      inference(symmetry,[status(thm)],[23])).
% 1.69/1.87  tff(25,plain,
% 1.69/1.87      (ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))) = ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))),
% 1.69/1.87      inference(monotonicity,[status(thm)],[24])).
% 1.69/1.87  tff(26,plain,
% 1.69/1.87      (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))),
% 1.69/1.87      inference(monotonicity,[status(thm)],[25])).
% 1.69/1.87  tff(27,plain,
% 1.69/1.87      (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))),
% 1.69/1.87      inference(symmetry,[status(thm)],[26])).
% 1.69/1.87  tff(28,plain,
% 1.69/1.87      (^[A_27a: del] : refl(mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))) <=> mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.69/1.87      inference(bind,[status(th)],[])).
% 1.69/1.87  tff(29,plain,
% 1.69/1.87      (![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))) <=> ![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))),
% 1.69/1.87      inference(quant_intro,[status(thm)],[28])).
% 1.69/1.87  tff(30,plain,
% 1.69/1.87      (![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))) <=> ![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))),
% 1.69/1.87      inference(rewrite,[status(thm)],[])).
% 1.69/1.87  tff(31,axiom,(![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Epred__set_2EREST')).
% 1.69/1.87  tff(32,plain,
% 1.69/1.87      (![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))),
% 1.69/1.87      inference(modus_ponens,[status(thm)],[31, 30])).
% 1.69/1.87  tff(33,plain,(
% 1.69/1.87      ![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))),
% 1.69/1.87      inference(skolemize,[status(sab)],[32])).
% 1.69/1.87  tff(34,plain,
% 1.69/1.87      (![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))),
% 1.69/1.87      inference(modus_ponens,[status(thm)],[33, 29])).
% 1.69/1.87  tff(35,plain,
% 1.69/1.87      ((~![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))) | mem(c_2Epred__set_2EREST(A_27a!4), arr(arr(A_27a!4, bool), arr(A_27a!4, bool)))),
% 1.69/1.87      inference(quant_inst,[status(thm)],[])).
% 1.69/1.87  tff(36,plain,
% 1.69/1.87      (mem(c_2Epred__set_2EREST(A_27a!4), arr(arr(A_27a!4, bool), arr(A_27a!4, bool)))),
% 1.69/1.87      inference(unit_resolution,[status(thm)],[35, 34])).
% 1.69/1.87  tff(37,plain,
% 1.69/1.87      (^[A: del, B: del, 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))))),
% 1.69/1.87      inference(bind,[status(th)],[])).
% 1.69/1.87  tff(38,plain,
% 1.69/1.87      (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.69/1.87      inference(quant_intro,[status(thm)],[37])).
% 1.69/1.87  tff(39,plain,
% 1.69/1.87      (^[A: del, B: del, 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))))),
% 1.69/1.87      inference(bind,[status(th)],[])).
% 1.69/1.87  tff(40,plain,
% 1.69/1.87      (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.69/1.87      inference(quant_intro,[status(thm)],[39])).
% 1.69/1.87  tff(41,plain,
% 1.69/1.87      (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.69/1.87      inference(transitivity,[status(thm)],[40, 38])).
% 1.69/1.87  tff(42,plain,
% 1.69/1.87      (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.69/1.87      inference(rewrite,[status(thm)],[])).
% 1.69/1.87  tff(43,plain,
% 1.69/1.87      (^[A: del, B: del, 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)))))),
% 1.69/1.87      inference(bind,[status(th)],[])).
% 1.69/1.87  tff(44,plain,
% 1.69/1.87      (![A: del, B: del, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.69/1.87      inference(quant_intro,[status(thm)],[43])).
% 1.69/1.87  tff(45,axiom,(![A: del, B: del, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B)))), file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001_2.ax','ap_tp')).
% 1.69/1.87  tff(46,plain,
% 1.69/1.87      (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.69/1.87      inference(modus_ponens,[status(thm)],[45, 44])).
% 1.69/1.87  tff(47,plain,
% 1.69/1.87      (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.69/1.87      inference(modus_ponens,[status(thm)],[46, 42])).
% 1.69/1.87  tff(48,plain,(
% 1.69/1.87      ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.69/1.87      inference(skolemize,[status(sab)],[47])).
% 1.69/1.87  tff(49,plain,
% 1.69/1.87      (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.69/1.87      inference(modus_ponens,[status(thm)],[48, 41])).
% 1.69/1.87  tff(50,plain,
% 1.69/1.87      (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2EREST(A_27a!4), arr(arr(A_27a!4, bool), arr(A_27a!4, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool))))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2EREST(A_27a!4), arr(arr(A_27a!4, bool), arr(A_27a!4, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool))))),
% 1.69/1.87      inference(rewrite,[status(thm)],[])).
% 1.69/1.87  tff(51,plain,
% 1.69/1.87      ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2EREST(A_27a!4), arr(arr(A_27a!4, bool), arr(A_27a!4, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool))))),
% 1.69/1.87      inference(quant_inst,[status(thm)],[])).
% 1.69/1.87  tff(52,plain,
% 1.69/1.87      ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2EREST(A_27a!4), arr(arr(A_27a!4, bool), arr(A_27a!4, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool)))),
% 1.69/1.87      inference(modus_ponens,[status(thm)],[51, 50])).
% 1.69/1.87  tff(53,plain,
% 1.69/1.87      (![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool)))),
% 1.69/1.87      inference(unit_resolution,[status(thm)],[52, 49, 36])).
% 1.69/1.87  tff(54,plain,
% 1.69/1.87      (((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool)))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool)))) <=> ((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool)))) | (~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool)))),
% 1.69/1.87      inference(rewrite,[status(thm)],[])).
% 1.69/1.87  tff(55,plain,
% 1.69/1.87      ((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool)))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool)))),
% 1.69/1.87      inference(quant_inst,[status(thm)],[])).
% 1.69/1.87  tff(56,plain,
% 1.69/1.87      ((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool)))) | (~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))),
% 1.69/1.87      inference(modus_ponens,[status(thm)],[55, 54])).
% 1.69/1.87  tff(57,plain,
% 1.69/1.87      (mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))),
% 1.69/1.87      inference(unit_resolution,[status(thm)],[56, 9, 53])).
% 1.69/1.87  tff(58,plain,
% 1.69/1.87      (^[A_27a: del, V0s: $i] : 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)))))) | (~(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))))))))))) <=> ((~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)))))))))))),
% 1.69/1.87      inference(bind,[status(th)],[])).
% 1.69/1.87  tff(59,plain,
% 1.69/1.87      (![A_27a: del, 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: del, 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))))))))))),
% 1.69/1.87      inference(quant_intro,[status(thm)],[58])).
% 1.69/1.87  tff(60,plain,
% 1.69/1.87      (^[A_27a: del, V0s: $i] : refl(((~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))))))))))) <=> ((~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))))))))))))),
% 1.69/1.87      inference(bind,[status(th)],[])).
% 1.69/1.87  tff(61,plain,
% 1.69/1.87      (![A_27a: del, 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: del, 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)))))))))))),
% 1.69/1.87      inference(quant_intro,[status(thm)],[60])).
% 1.69/1.87  tff(62,plain,
% 1.69/1.87      (^[A_27a: del, V0s: $i] : 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)))))) | (~(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))))))))))) <=> ((~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))))))))))))),
% 1.69/1.87      inference(bind,[status(th)],[])).
% 1.69/1.87  tff(63,plain,
% 1.69/1.87      (![A_27a: del, 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: del, 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)))))))))))),
% 1.69/1.87      inference(quant_intro,[status(thm)],[62])).
% 1.69/1.87  tff(64,plain,
% 1.69/1.87      (![A_27a: del, 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: del, 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)))))))))))),
% 1.69/1.87      inference(transitivity,[status(thm)],[63, 61])).
% 1.69/1.87  tff(65,plain,
% 1.69/1.87      (^[A_27a: del, V0s: $i] : 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))))) & (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))))))))) <=> ((~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))))))))))))),
% 1.69/1.87      inference(bind,[status(th)],[])).
% 1.69/1.87  tff(66,plain,
% 1.69/1.87      (![A_27a: del, 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: del, 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)))))))))))),
% 1.69/1.87      inference(quant_intro,[status(thm)],[65])).
% 1.69/1.87  tff(67,plain,
% 1.69/1.87      (![A_27a: del, 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: del, 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)))))))),
% 1.69/1.87      inference(rewrite,[status(thm)],[])).
% 1.69/1.87  tff(68,plain,
% 1.69/1.87      (^[A_27a: del, 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)))))))))),
% 1.69/1.87      inference(bind,[status(th)],[])).
% 1.69/1.87  tff(69,plain,
% 1.69/1.87      (![A_27a: del, 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: del, 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)))))))),
% 1.69/1.87      inference(quant_intro,[status(thm)],[68])).
% 1.69/1.87  tff(70,axiom,(![A_27a: del, 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/sandbox2/benchmark/theBenchmark.p','ax_thm_2Epred__set_2ESUBSET__DEF')).
% 1.69/1.87  tff(71,plain,
% 1.69/1.87      (![A_27a: del, 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)))))))),
% 1.69/1.87      inference(modus_ponens,[status(thm)],[70, 69])).
% 1.69/1.87  tff(72,plain,
% 1.69/1.87      (![A_27a: del, 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)))))))),
% 1.69/1.87      inference(modus_ponens,[status(thm)],[71, 67])).
% 1.69/1.87  tff(73,plain,(
% 1.69/1.87      ![A_27a: del, 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)))))))))),
% 1.69/1.87      inference(skolemize,[status(sab)],[72])).
% 1.69/1.87  tff(74,plain,
% 1.69/1.87      (![A_27a: del, 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)))))))))))),
% 1.69/1.87      inference(modus_ponens,[status(thm)],[73, 66])).
% 1.69/1.87  tff(75,plain,
% 1.69/1.87      (![A_27a: del, 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)))))))))))),
% 1.69/1.87      inference(modus_ponens,[status(thm)],[74, 64])).
% 1.69/1.87  tff(76,plain,
% 1.69/1.87      (![A_27a: del, 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))))))))))),
% 1.69/1.87      inference(modus_ponens,[status(thm)],[75, 59])).
% 1.69/1.87  tff(77,plain,
% 1.69/1.87      (((~![A_27a: del, 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))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))) <=> ((~![A_27a: del, 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))))))))))) | (~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))),
% 1.69/1.87      inference(rewrite,[status(thm)],[])).
% 1.69/1.87  tff(78,plain,
% 1.69/1.87      (((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~mem(V2x, A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) <=> ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))),
% 1.69/1.87      inference(rewrite,[status(thm)],[])).
% 1.69/1.87  tff(79,plain,
% 1.69/1.87      (((~![A_27a: del, 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))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~mem(V2x, A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))) <=> ((~![A_27a: del, 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))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))))),
% 1.69/1.87      inference(monotonicity,[status(thm)],[78])).
% 1.69/1.87  tff(80,plain,
% 1.69/1.87      (((~![A_27a: del, 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))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~mem(V2x, A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))) <=> ((~![A_27a: del, 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))))))))))) | (~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))),
% 1.69/1.88      inference(transitivity,[status(thm)],[79, 77])).
% 1.69/1.88  tff(81,plain,
% 1.69/1.88      ((~![A_27a: del, 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))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~mem(V2x, A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))),
% 1.69/1.88      inference(quant_inst,[status(thm)],[])).
% 1.69/1.88  tff(82,plain,
% 1.69/1.88      ((~![A_27a: del, 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))))))))))) | (~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))),
% 1.69/1.88      inference(modus_ponens,[status(thm)],[81, 80])).
% 1.69/1.88  tff(83,plain,
% 1.69/1.88      ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))),
% 1.69/1.88      inference(unit_resolution,[status(thm)],[82, 76])).
% 1.69/1.88  tff(84,plain,
% 1.69/1.88      (![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))),
% 1.69/1.88      inference(unit_resolution,[status(thm)],[83, 57])).
% 1.69/1.88  tff(85,plain,
% 1.69/1.88      (((~![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))) <=> ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) | (~mem(V0s!3, arr(A_27a!4, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))),
% 1.69/1.88      inference(rewrite,[status(thm)],[])).
% 1.69/1.88  tff(86,plain,
% 1.69/1.88      (((~mem(V0s!3, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))) <=> ((~mem(V0s!3, arr(A_27a!4, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))),
% 1.69/1.88      inference(rewrite,[status(thm)],[])).
% 1.69/1.88  tff(87,plain,
% 1.69/1.88      (((~![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) <=> ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))))),
% 1.69/1.88      inference(monotonicity,[status(thm)],[86])).
% 1.69/1.88  tff(88,plain,
% 1.69/1.88      (((~![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) <=> ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) | (~mem(V0s!3, arr(A_27a!4, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))),
% 1.69/1.88      inference(transitivity,[status(thm)],[87, 85])).
% 1.69/1.88  tff(89,plain,
% 1.69/1.88      ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))),
% 1.69/1.88      inference(quant_inst,[status(thm)],[])).
% 1.69/1.88  tff(90,plain,
% 1.69/1.88      ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) | (~mem(V0s!3, arr(A_27a!4, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))),
% 1.69/1.88      inference(modus_ponens,[status(thm)],[89, 88])).
% 1.69/1.88  tff(91,plain,
% 1.69/1.88      (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))),
% 1.69/1.88      inference(unit_resolution,[status(thm)],[90, 9, 84])).
% 1.69/1.88  tff(92,plain,
% 1.69/1.88      (((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))),
% 1.69/1.88      inference(tautology,[status(thm)],[])).
% 1.69/1.88  tff(93,plain,
% 1.69/1.88      (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))),
% 1.69/1.88      inference(unit_resolution,[status(thm)],[92, 91])).
% 1.69/1.88  tff(94,plain,
% 1.69/1.88      (~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))),
% 1.69/1.88      inference(or_elim,[status(thm)],[8])).
% 1.69/1.88  tff(95,plain,
% 1.69/1.88      ((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))),
% 1.69/1.88      inference(tautology,[status(thm)],[])).
% 1.69/1.88  tff(96,plain,
% 1.69/1.88      ((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))),
% 1.69/1.88      inference(unit_resolution,[status(thm)],[95, 94])).
% 1.69/1.88  tff(97,plain,
% 1.69/1.88      (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))),
% 1.69/1.88      inference(unit_resolution,[status(thm)],[96, 93])).
% 1.69/1.88  tff(98,plain,
% 1.69/1.88      ((p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))),
% 1.69/1.88      inference(tautology,[status(thm)],[])).
% 1.69/1.88  tff(99,plain,
% 1.69/1.88      (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))),
% 1.69/1.88      inference(unit_resolution,[status(thm)],[98, 97])).
% 1.69/1.88  tff(100,plain,
% 1.69/1.88      (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))),
% 1.69/1.88      inference(modus_ponens,[status(thm)],[99, 27])).
% 1.69/1.88  tff(101,plain,
% 1.69/1.88      ((p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))) | mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)),
% 1.69/1.88      inference(tautology,[status(thm)],[])).
% 1.69/1.88  tff(102,plain,
% 1.69/1.88      (mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)),
% 1.69/1.89      inference(unit_resolution,[status(thm)],[101, 97])).
% 1.69/1.89  tff(103,plain,
% 1.69/1.89      (^[A_27a: del, V0s: $i] : refl(((~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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))))),
% 1.69/1.89      inference(bind,[status(th)],[])).
% 1.69/1.89  tff(104,plain,
% 1.69/1.89      (![A_27a: del, 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))) <=> ![A_27a: del, 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))),
% 1.69/1.89      inference(quant_intro,[status(thm)],[103])).
% 1.69/1.89  tff(105,plain,
% 1.69/1.89      (^[A_27a: del, V0s: $i] : 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))))),
% 1.69/1.89      inference(bind,[status(th)],[])).
% 1.69/1.89  tff(106,plain,
% 1.69/1.89      (![A_27a: del, 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))) <=> ![A_27a: del, 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))),
% 1.69/1.89      inference(quant_intro,[status(thm)],[105])).
% 1.69/1.89  tff(107,plain,
% 1.69/1.89      (![A_27a: del, 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))) <=> ![A_27a: del, 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))),
% 1.69/1.89      inference(transitivity,[status(thm)],[106, 104])).
% 1.69/1.89  tff(108,plain,
% 1.69/1.89      (^[A_27a: del, V0s: $i] : 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))))),
% 1.69/1.89      inference(bind,[status(th)],[])).
% 1.69/1.89  tff(109,plain,
% 1.69/1.89      (![A_27a: del, 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: del, 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))),
% 1.69/1.89      inference(quant_intro,[status(thm)],[108])).
% 1.69/1.89  tff(110,plain,
% 1.69/1.89      (![A_27a: del, 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: del, 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)))))))),
% 1.69/1.89      inference(rewrite,[status(thm)],[])).
% 1.69/1.89  tff(111,plain,
% 1.69/1.89      (^[A_27a: del, 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)))))))))),
% 1.69/1.89      inference(bind,[status(th)],[])).
% 1.69/1.89  tff(112,plain,
% 1.69/1.89      (![A_27a: del, 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: del, 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)))))))),
% 1.69/1.89      inference(quant_intro,[status(thm)],[111])).
% 1.69/1.89  tff(113,axiom,(![A_27a: del, 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/sandbox2/benchmark/theBenchmark.p','conj_thm_2Epred__set_2EIN__DELETE')).
% 1.69/1.89  tff(114,plain,
% 1.69/1.89      (![A_27a: del, 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)))))))),
% 1.69/1.89      inference(modus_ponens,[status(thm)],[113, 112])).
% 1.69/1.89  tff(115,plain,
% 1.69/1.89      (![A_27a: del, 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)))))))),
% 1.69/1.89      inference(modus_ponens,[status(thm)],[114, 110])).
% 1.69/1.89  tff(116,plain,(
% 1.69/1.89      ![A_27a: del, 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)))))))),
% 1.69/1.89      inference(skolemize,[status(sab)],[115])).
% 1.69/1.89  tff(117,plain,
% 1.69/1.89      (![A_27a: del, 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))),
% 1.69/1.89      inference(modus_ponens,[status(thm)],[116, 109])).
% 1.69/1.89  tff(118,plain,
% 1.69/1.89      (![A_27a: del, 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))),
% 1.69/1.89      inference(modus_ponens,[status(thm)],[117, 107])).
% 1.69/1.89  tff(119,plain,
% 1.69/1.89      (((~![A_27a: del, 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))))))))) <=> ((~![A_27a: del, 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))) | (~mem(V0s!3, arr(A_27a!4, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))))))))),
% 1.69/1.89      inference(rewrite,[status(thm)],[])).
% 1.69/1.89  tff(120,plain,
% 1.69/1.89      ((~![A_27a: del, 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))))))))),
% 1.69/1.89      inference(quant_inst,[status(thm)],[])).
% 1.69/1.89  tff(121,plain,
% 1.69/1.89      ((~![A_27a: del, 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), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))) | (~mem(V0s!3, arr(A_27a!4, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y)))))))),
% 1.69/1.89      inference(modus_ponens,[status(thm)],[120, 119])).
% 1.69/1.89  tff(122,plain,
% 1.69/1.89      (![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y)))))))),
% 1.69/1.89      inference(unit_resolution,[status(thm)],[121, 118, 9])).
% 1.69/1.89  tff(123,plain,
% 1.69/1.89      (((~![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y)))))))) | ((~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y)))))))) <=> ((~![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y)))))))) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y)))))))),
% 1.69/1.89      inference(rewrite,[status(thm)],[])).
% 1.69/1.89  tff(124,plain,
% 1.69/1.89      ((~![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y)))))))) | ((~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y)))))))),
% 1.69/1.89      inference(quant_inst,[status(thm)],[])).
% 1.69/1.89  tff(125,plain,
% 1.69/1.89      ((~![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y)))))))) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))))))),
% 1.69/1.89      inference(modus_ponens,[status(thm)],[124, 123])).
% 1.69/1.89  tff(126,plain,
% 1.69/1.89      (![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))))))),
% 1.69/1.89      inference(unit_resolution,[status(thm)],[125, 122, 102])).
% 1.69/1.89  tff(127,plain,
% 1.69/1.89      (^[A_27a: del] : refl(mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)) <=> mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.69/1.89      inference(bind,[status(th)],[])).
% 1.69/1.89  tff(128,plain,
% 1.69/1.89      (![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)) <=> ![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))),
% 1.69/1.89      inference(quant_intro,[status(thm)],[127])).
% 1.69/1.89  tff(129,plain,
% 1.69/1.89      (![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)) <=> ![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))),
% 1.69/1.89      inference(rewrite,[status(thm)],[])).
% 1.69/1.89  tff(130,axiom,(![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Epred__set_2ECHOICE')).
% 1.69/1.89  tff(131,plain,
% 1.69/1.89      (![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))),
% 1.69/1.89      inference(modus_ponens,[status(thm)],[130, 129])).
% 1.69/1.89  tff(132,plain,(
% 1.69/1.89      ![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))),
% 1.69/1.89      inference(skolemize,[status(sab)],[131])).
% 1.69/1.89  tff(133,plain,
% 1.69/1.89      (![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))),
% 1.69/1.89      inference(modus_ponens,[status(thm)],[132, 128])).
% 1.69/1.89  tff(134,plain,
% 1.69/1.89      ((~![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))) | mem(c_2Epred__set_2ECHOICE(A_27a!4), arr(arr(A_27a!4, bool), A_27a!4))),
% 1.69/1.89      inference(quant_inst,[status(thm)],[])).
% 1.69/1.89  tff(135,plain,
% 1.69/1.89      (mem(c_2Epred__set_2ECHOICE(A_27a!4), arr(arr(A_27a!4, bool), A_27a!4))),
% 1.69/1.89      inference(unit_resolution,[status(thm)],[134, 133])).
% 1.69/1.89  tff(136,plain,
% 1.69/1.89      (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2ECHOICE(A_27a!4), arr(arr(A_27a!4, bool), A_27a!4))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4)))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2ECHOICE(A_27a!4), arr(arr(A_27a!4, bool), A_27a!4))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4)))),
% 1.69/1.89      inference(rewrite,[status(thm)],[])).
% 1.69/1.89  tff(137,plain,
% 1.69/1.89      ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2ECHOICE(A_27a!4), arr(arr(A_27a!4, bool), A_27a!4))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4)))),
% 1.69/1.89      inference(quant_inst,[status(thm)],[])).
% 1.69/1.89  tff(138,plain,
% 1.69/1.89      ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2ECHOICE(A_27a!4), arr(arr(A_27a!4, bool), A_27a!4))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4))),
% 1.69/1.89      inference(modus_ponens,[status(thm)],[137, 136])).
% 1.69/1.89  tff(139,plain,
% 1.69/1.89      (![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4))),
% 1.69/1.89      inference(unit_resolution,[status(thm)],[138, 49, 135])).
% 1.69/1.89  tff(140,plain,
% 1.69/1.89      (((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4))) <=> ((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4))) | (~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4))),
% 1.69/1.89      inference(rewrite,[status(thm)],[])).
% 1.69/1.89  tff(141,plain,
% 1.69/1.89      ((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4))),
% 1.69/1.89      inference(quant_inst,[status(thm)],[])).
% 1.69/1.89  tff(142,plain,
% 1.69/1.89      ((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4))) | (~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4)),
% 1.69/1.89      inference(modus_ponens,[status(thm)],[141, 140])).
% 1.69/1.89  tff(143,plain,
% 1.69/1.89      (mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4)),
% 1.69/1.89      inference(unit_resolution,[status(thm)],[142, 9, 139])).
% 1.69/1.89  tff(144,plain,
% 1.69/1.89      (((~![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))))))) | ((~mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))))))) <=> ((~![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))))))) | (~mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))))))),
% 1.69/1.89      inference(rewrite,[status(thm)],[])).
% 1.69/1.89  tff(145,plain,
% 1.69/1.89      ((~![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))))))) | ((~mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))))))),
% 1.69/1.89      inference(quant_inst,[status(thm)],[])).
% 1.69/1.89  tff(146,plain,
% 1.69/1.89      ((~![V2y: $i] : ((~mem(V2y, A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))))))) | (~mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))))),
% 1.69/1.89      inference(modus_ponens,[status(thm)],[145, 144])).
% 1.69/1.89  tff(147,plain,
% 1.69/1.89      (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))))),
% 1.69/1.89      inference(unit_resolution,[status(thm)],[146, 143, 126])).
% 1.69/1.89  tff(148,plain,
% 1.69/1.89      ((p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)))),
% 1.69/1.89      inference(tautology,[status(thm)],[])).
% 1.69/1.89  tff(149,plain,
% 1.69/1.89      (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))),
% 1.69/1.89      inference(unit_resolution,[status(thm)],[148, 97])).
% 1.69/1.89  tff(150,plain,
% 1.69/1.89      (((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))),
% 1.69/1.90      inference(tautology,[status(thm)],[])).
% 1.69/1.90  tff(151,plain,
% 1.69/1.90      ((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))),
% 1.69/1.90      inference(unit_resolution,[status(thm)],[150, 149])).
% 1.69/1.90  tff(152,plain,
% 1.69/1.90      ((((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))))),
% 1.69/1.90      inference(tautology,[status(thm)],[])).
% 1.69/1.90  tff(153,plain,
% 1.69/1.90      ((((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))))),
% 1.69/1.90      inference(unit_resolution,[status(thm)],[152, 151])).
% 1.69/1.90  tff(154,plain,
% 1.69/1.90      (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))),
% 1.69/1.90      inference(unit_resolution,[status(thm)],[153, 147])).
% 1.69/1.90  tff(155,plain,
% 1.69/1.90      ($false),
% 1.69/1.90      inference(unit_resolution,[status(thm)],[154, 100])).
% 1.69/1.90  % SZS output end Proof
% 1.69/1.90  % E exiting
%------------------------------------------------------------------------------