Z3---4.15.1.THM-Prf.s

%------------------------------------------------------------------------------
% 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 : n012.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 1.53s 1.69s
% Output   : Proof 1.53s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : ITP004+2 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.06/0.12  % Command    : run_E %s %d THM
% 0.11/0.33  % Computer : n012.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Thu Jun 19 18:02:56 EDT 2025
% 0.11/0.33  % CPUTime    : 
% 1.53/1.69  % SZS status Theorem
% 1.53/1.69  % SZS output start Proof
% 1.53/1.69  tff(p_type, type, (
% 1.53/1.69     p: $i > $o)).
% 1.53/1.69  tff(ap_type, type, (
% 1.53/1.69     ap: ( $i * $i ) > $i)).
% 1.53/1.69  tff(tptp_fun_V0s_4_type, type, (
% 1.53/1.69     tptp_fun_V0s_4: $i)).
% 1.53/1.69  tff(c_2Epred__set_2ECHOICE_type, type, (
% 1.53/1.69     c_2Epred__set_2ECHOICE: $i > $i)).
% 1.53/1.69  tff(tptp_fun_A_27a_3_type, type, (
% 1.53/1.69     tptp_fun_A_27a_3: $i)).
% 1.53/1.69  tff(c_2Epred__set_2EDELETE_type, type, (
% 1.53/1.69     c_2Epred__set_2EDELETE: $i > $i)).
% 1.53/1.69  tff(tptp_fun_V2x_2_type, type, (
% 1.53/1.69     tptp_fun_V2x_2: ( $i * $i * $i ) > $i)).
% 1.53/1.69  tff(c_2Epred__set_2EREST_type, type, (
% 1.53/1.69     c_2Epred__set_2EREST: $i > $i)).
% 1.53/1.69  tff(c_2Ebool_2EIN_type, type, (
% 1.53/1.69     c_2Ebool_2EIN: $i > $i)).
% 1.53/1.69  tff(mem_type, type, (
% 1.53/1.69     mem: ( $i * $i ) > $o)).
% 1.53/1.69  tff(arr_type, type, (
% 1.53/1.69     arr: ( $i * $i ) > $i)).
% 1.53/1.69  tff(bool_type, type, (
% 1.53/1.69     bool: $i)).
% 1.53/1.69  tff(ne_type, type, (
% 1.53/1.69     ne: $i > $o)).
% 1.53/1.69  tff(c_2Epred__set_2ESUBSET_type, type, (
% 1.53/1.69     c_2Epred__set_2ESUBSET: $i > $i)).
% 1.53/1.69  tff(1,plain,
% 1.53/1.69      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))) <=> (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))))),
% 1.53/1.69      inference(rewrite,[status(thm)],[])).
% 1.53/1.69  tff(2,plain,
% 1.53/1.69      ((~![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))) <=> (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))))),
% 1.53/1.69      inference(rewrite,[status(thm)],[])).
% 1.53/1.69  tff(3,axiom,(~![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_thm_2Epred__set_2EREST__SUBSET')).
% 1.53/1.69  tff(4,plain,
% 1.53/1.69      (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))),
% 1.53/1.69      inference(modus_ponens,[status(thm)],[3, 2])).
% 1.53/1.69  tff(5,plain,
% 1.53/1.69      (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))),
% 1.53/1.69      inference(modus_ponens,[status(thm)],[4, 1])).
% 1.53/1.69  tff(6,plain,
% 1.53/1.69      (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))),
% 1.53/1.69      inference(modus_ponens,[status(thm)],[5, 1])).
% 1.53/1.69  tff(7,plain,
% 1.53/1.69      (~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))),
% 1.53/1.69      inference(modus_ponens,[status(thm)],[6, 1])).
% 1.53/1.69  tff(8,plain,
% 1.53/1.69      (ne(A_27a!3)),
% 1.53/1.69      inference(and_elim,[status(thm)],[7])).
% 1.53/1.69  tff(9,plain,
% 1.53/1.69      (^[A_27a: $i] : refl(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))))),
% 1.53/1.69      inference(bind,[status(th)],[])).
% 1.53/1.69  tff(10,plain,
% 1.53/1.69      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.53/1.69      inference(quant_intro,[status(thm)],[9])).
% 1.53/1.69  tff(11,plain,
% 1.53/1.69      (^[A_27a: $i] : rewrite(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))))),
% 1.53/1.69      inference(bind,[status(th)],[])).
% 1.53/1.69  tff(12,plain,
% 1.53/1.69      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.53/1.69      inference(quant_intro,[status(thm)],[11])).
% 1.53/1.69  tff(13,plain,
% 1.53/1.69      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.53/1.69      inference(transitivity,[status(thm)],[12, 10])).
% 1.53/1.69  tff(14,plain,
% 1.53/1.69      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.53/1.69      inference(rewrite,[status(thm)],[])).
% 1.53/1.69  tff(15,plain,
% 1.53/1.69      (^[A_27a: $i] : trans(monotonicity(quant_intro(proof_bind(^[V0s: $i] : rewrite((mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))) <=> ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))), (![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))) <=> ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))), ((ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> (ne(A_27a) => ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))))), rewrite((ne(A_27a) => ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))), ((ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))))),
% 1.53/1.69      inference(bind,[status(th)],[])).
% 1.53/1.69  tff(16,plain,
% 1.53/1.69      (![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.53/1.69      inference(quant_intro,[status(thm)],[15])).
% 1.53/1.69  tff(17,axiom,(![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax_thm_2Epred__set_2EREST__DEF')).
% 1.53/1.69  tff(18,plain,
% 1.53/1.69      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.53/1.69      inference(modus_ponens,[status(thm)],[17, 16])).
% 1.53/1.69  tff(19,plain,
% 1.53/1.69      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.53/1.69      inference(modus_ponens,[status(thm)],[18, 14])).
% 1.53/1.69  tff(20,plain,(
% 1.53/1.69      ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.53/1.69      inference(skolemize,[status(sab)],[19])).
% 1.53/1.69  tff(21,plain,
% 1.53/1.69      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 1.53/1.69      inference(modus_ponens,[status(thm)],[20, 13])).
% 1.53/1.69  tff(22,plain,
% 1.53/1.69      (((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s)))))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s)))))),
% 1.53/1.69      inference(rewrite,[status(thm)],[])).
% 1.53/1.69  tff(23,plain,
% 1.53/1.69      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s)))))),
% 1.53/1.69      inference(quant_inst,[status(thm)],[])).
% 1.53/1.69  tff(24,plain,
% 1.53/1.69      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s))))),
% 1.53/1.69      inference(modus_ponens,[status(thm)],[23, 22])).
% 1.53/1.69  tff(25,plain,
% 1.53/1.69      (![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s))))),
% 1.53/1.69      inference(unit_resolution,[status(thm)],[24, 21, 8])).
% 1.53/1.69  tff(26,plain,
% 1.53/1.69      (~((~mem(V0s!4, arr(A_27a!3, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)))),
% 1.53/1.69      inference(and_elim,[status(thm)],[7])).
% 1.53/1.69  tff(27,plain,
% 1.53/1.69      (mem(V0s!4, arr(A_27a!3, bool))),
% 1.53/1.69      inference(or_elim,[status(thm)],[26])).
% 1.53/1.69  tff(28,plain,
% 1.53/1.69      (((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s!4) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))) <=> ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s))))) | (~mem(V0s!4, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s!4) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))),
% 1.53/1.69      inference(rewrite,[status(thm)],[])).
% 1.53/1.69  tff(29,plain,
% 1.53/1.69      ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s!4) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))),
% 1.53/1.69      inference(quant_inst,[status(thm)],[])).
% 1.53/1.69  tff(30,plain,
% 1.53/1.69      ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s))))) | (~mem(V0s!4, arr(A_27a!3, bool))) | (ap(c_2Epred__set_2EREST(A_27a!3), V0s!4) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))),
% 1.53/1.69      inference(modus_ponens,[status(thm)],[29, 28])).
% 1.53/1.69  tff(31,plain,
% 1.53/1.69      (ap(c_2Epred__set_2EREST(A_27a!3), V0s!4) = ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))),
% 1.53/1.69      inference(unit_resolution,[status(thm)],[30, 27, 25])).
% 1.53/1.69  tff(32,plain,
% 1.53/1.69      (ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)) = ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)),
% 1.53/1.69      inference(symmetry,[status(thm)],[31])).
% 1.53/1.69  tff(33,plain,
% 1.53/1.69      (ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))) = ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))),
% 1.53/1.69      inference(monotonicity,[status(thm)],[32])).
% 1.53/1.69  tff(34,plain,
% 1.53/1.69      (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))),
% 1.53/1.69      inference(monotonicity,[status(thm)],[33])).
% 1.53/1.69  tff(35,plain,
% 1.53/1.69      (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))),
% 1.53/1.69      inference(symmetry,[status(thm)],[34])).
% 1.53/1.69  tff(36,plain,
% 1.53/1.69      (^[A_27a: $i] : refl(((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))) <=> ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))))),
% 1.53/1.69      inference(bind,[status(th)],[])).
% 1.53/1.69  tff(37,plain,
% 1.53/1.69      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))) <=> ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.53/1.69      inference(quant_intro,[status(thm)],[36])).
% 1.53/1.69  tff(38,plain,
% 1.53/1.69      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))) <=> ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.53/1.69      inference(rewrite,[status(thm)],[])).
% 1.53/1.69  tff(39,plain,
% 1.53/1.69      (^[A_27a: $i] : rewrite((ne(A_27a) => mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))) <=> ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))))),
% 1.53/1.70      inference(bind,[status(th)],[])).
% 1.53/1.70  tff(40,plain,
% 1.53/1.70      (![A_27a: $i] : (ne(A_27a) => mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))) <=> ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.53/1.70      inference(quant_intro,[status(thm)],[39])).
% 1.53/1.70  tff(41,axiom,(![A_27a: $i] : (ne(A_27a) => mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mem_c_2Epred__set_2EREST')).
% 1.53/1.70  tff(42,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[41, 40])).
% 1.53/1.70  tff(43,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[42, 38])).
% 1.53/1.70  tff(44,plain,(
% 1.53/1.70      ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.53/1.70      inference(skolemize,[status(sab)],[43])).
% 1.53/1.70  tff(45,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[44, 37])).
% 1.53/1.70  tff(46,plain,
% 1.53/1.70      (((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))) | ((~ne(A_27a!3)) | mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool))))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))) | (~ne(A_27a!3)) | mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool))))),
% 1.53/1.70      inference(rewrite,[status(thm)],[])).
% 1.53/1.70  tff(47,plain,
% 1.53/1.70      ((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))) | ((~ne(A_27a!3)) | mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool))))),
% 1.53/1.70      inference(quant_inst,[status(thm)],[])).
% 1.53/1.70  tff(48,plain,
% 1.53/1.70      ((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))) | (~ne(A_27a!3)) | mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool)))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[47, 46])).
% 1.53/1.70  tff(49,plain,
% 1.53/1.70      (mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool)))),
% 1.53/1.70      inference(unit_resolution,[status(thm)],[48, 45, 8])).
% 1.53/1.70  tff(50,plain,
% 1.53/1.70      (^[A: $i, B: $i, F: $i] : refl(((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))),
% 1.53/1.70      inference(bind,[status(th)],[])).
% 1.53/1.70  tff(51,plain,
% 1.53/1.70      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.53/1.70      inference(quant_intro,[status(thm)],[50])).
% 1.53/1.70  tff(52,plain,
% 1.53/1.70      (^[A: $i, B: $i, F: $i] : rewrite(((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))),
% 1.53/1.70      inference(bind,[status(th)],[])).
% 1.53/1.70  tff(53,plain,
% 1.53/1.70      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.53/1.70      inference(quant_intro,[status(thm)],[52])).
% 1.53/1.70  tff(54,plain,
% 1.53/1.70      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.53/1.70      inference(transitivity,[status(thm)],[53, 51])).
% 1.53/1.70  tff(55,plain,
% 1.53/1.70      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.53/1.70      inference(rewrite,[status(thm)],[])).
% 1.53/1.70  tff(56,plain,
% 1.53/1.70      (^[A: $i, B: $i, F: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite((mem(X, A) => mem(ap(F, X), B)) <=> ((~mem(X, A)) | mem(ap(F, X), B)))), (![X: $i] : (mem(X, A) => mem(ap(F, X), B)) <=> ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))), ((mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> (mem(F, arr(A, B)) => ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))), rewrite((mem(F, arr(A, B)) => ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))), ((mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))))),
% 1.53/1.70      inference(bind,[status(th)],[])).
% 1.53/1.70  tff(57,plain,
% 1.53/1.70      (![A: $i, B: $i, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> ![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.53/1.70      inference(quant_intro,[status(thm)],[56])).
% 1.53/1.70  tff(58,axiom,(![A: $i, B: $i, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B)))), file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax','ap_tp')).
% 1.53/1.70  tff(59,plain,
% 1.53/1.70      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[58, 57])).
% 1.53/1.70  tff(60,plain,
% 1.53/1.70      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[59, 55])).
% 1.53/1.70  tff(61,plain,(
% 1.53/1.70      ![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.53/1.70      inference(skolemize,[status(sab)],[60])).
% 1.53/1.70  tff(62,plain,
% 1.53/1.70      (![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[61, 54])).
% 1.53/1.70  tff(63,plain,
% 1.53/1.70      (((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool))))) <=> ((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool))))),
% 1.53/1.70      inference(rewrite,[status(thm)],[])).
% 1.53/1.70  tff(64,plain,
% 1.53/1.70      ((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool))))),
% 1.53/1.70      inference(quant_inst,[status(thm)],[])).
% 1.53/1.70  tff(65,plain,
% 1.53/1.70      ((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2EREST(A_27a!3), arr(arr(A_27a!3, bool), arr(A_27a!3, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool)))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[64, 63])).
% 1.53/1.70  tff(66,plain,
% 1.53/1.70      (![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool)))),
% 1.53/1.70      inference(unit_resolution,[status(thm)],[65, 62, 49])).
% 1.53/1.70  tff(67,plain,
% 1.53/1.70      (((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool)))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool)))) <=> ((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool)))) | (~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool)))),
% 1.53/1.70      inference(rewrite,[status(thm)],[])).
% 1.53/1.70  tff(68,plain,
% 1.53/1.70      ((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool)))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool)))),
% 1.53/1.70      inference(quant_inst,[status(thm)],[])).
% 1.53/1.70  tff(69,plain,
% 1.53/1.70      ((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), X), arr(A_27a!3, bool)))) | (~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[68, 67])).
% 1.53/1.70  tff(70,plain,
% 1.53/1.70      (mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))),
% 1.53/1.70      inference(unit_resolution,[status(thm)],[69, 27, 66])).
% 1.53/1.70  tff(71,plain,
% 1.53/1.70      (^[A_27a: $i] : rewrite(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))))),
% 1.53/1.70      inference(bind,[status(th)],[])).
% 1.53/1.70  tff(72,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))),
% 1.53/1.70      inference(quant_intro,[status(thm)],[71])).
% 1.53/1.70  tff(73,plain,
% 1.53/1.70      (^[A_27a: $i] : refl(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))))),
% 1.53/1.70      inference(bind,[status(th)],[])).
% 1.53/1.70  tff(74,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 1.53/1.70      inference(quant_intro,[status(thm)],[73])).
% 1.53/1.70  tff(75,plain,
% 1.53/1.70      (^[A_27a: $i] : rewrite(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))))),
% 1.53/1.70      inference(bind,[status(th)],[])).
% 1.53/1.70  tff(76,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 1.53/1.70      inference(quant_intro,[status(thm)],[75])).
% 1.53/1.70  tff(77,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 1.53/1.70      inference(transitivity,[status(thm)],[76, 74])).
% 1.53/1.70  tff(78,plain,
% 1.53/1.70      (^[A_27a: $i] : rewrite(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))) & (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))))),
% 1.53/1.70      inference(bind,[status(th)],[])).
% 1.53/1.70  tff(79,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))) & (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 1.53/1.70      inference(quant_intro,[status(thm)],[78])).
% 1.53/1.70  tff(80,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))),
% 1.53/1.70      inference(rewrite,[status(thm)],[])).
% 1.53/1.70  tff(81,plain,
% 1.53/1.70      (^[A_27a: $i] : trans(monotonicity(quant_intro(proof_bind(^[V0s: $i] : trans(monotonicity(quant_intro(proof_bind(^[V1t: $i] : trans(monotonicity(rewrite((p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))) <=> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))), ((mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))) <=> (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))), rewrite((mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) <=> ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))), ((mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))) <=> ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))), (![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))) <=> ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))), ((mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))))) <=> (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))), rewrite((mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))), ((mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))), (![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))))) <=> ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))), ((ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))))) <=> (ne(A_27a) => ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))), rewrite((ne(A_27a) => ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))), ((ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))),
% 1.53/1.70      inference(bind,[status(th)],[])).
% 1.53/1.70  tff(82,plain,
% 1.53/1.70      (![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))),
% 1.53/1.70      inference(quant_intro,[status(thm)],[81])).
% 1.53/1.70  tff(83,axiom,(![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax_thm_2Epred__set_2ESUBSET__DEF')).
% 1.53/1.70  tff(84,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[83, 82])).
% 1.53/1.70  tff(85,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[84, 80])).
% 1.53/1.70  tff(86,plain,(
% 1.53/1.70      ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))) & (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))),
% 1.53/1.70      inference(skolemize,[status(sab)],[85])).
% 1.53/1.70  tff(87,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[86, 79])).
% 1.53/1.70  tff(88,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[87, 77])).
% 1.53/1.70  tff(89,plain,
% 1.53/1.70      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))),
% 1.53/1.70      inference(modus_ponens,[status(thm)],[88, 72])).
% 1.53/1.70  tff(90,plain,
% 1.53/1.70      (((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))),
% 1.53/1.70      inference(rewrite,[status(thm)],[])).
% 1.53/1.70  tff(91,plain,
% 1.53/1.70      (((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~mem(V2x, A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) <=> ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))),
% 1.53/1.70      inference(rewrite,[status(thm)],[])).
% 1.53/1.70  tff(92,plain,
% 1.53/1.70      (((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~mem(V2x, A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))))),
% 1.53/1.70      inference(monotonicity,[status(thm)],[91])).
% 1.53/1.70  tff(93,plain,
% 1.53/1.70      (((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~mem(V2x, A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))),
% 1.53/1.70      inference(transitivity,[status(thm)],[92, 90])).
% 1.53/1.70  tff(94,plain,
% 1.53/1.70      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~mem(V2x, A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s)))))))))))),
% 1.53/1.70      inference(quant_inst,[status(thm)],[])).
% 1.53/1.70  tff(95,plain,
% 1.53/1.70      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))),
% 1.53/1.71      inference(modus_ponens,[status(thm)],[94, 93])).
% 1.53/1.71  tff(96,plain,
% 1.53/1.71      (![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))),
% 1.53/1.71      inference(unit_resolution,[status(thm)],[95, 89, 8])).
% 1.53/1.71  tff(97,plain,
% 1.53/1.71      (((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))))) <=> ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) | (~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))))),
% 1.53/1.71      inference(rewrite,[status(thm)],[])).
% 1.53/1.71  tff(98,plain,
% 1.53/1.71      (((~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))) <=> ((~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))))),
% 1.53/1.71      inference(rewrite,[status(thm)],[])).
% 1.53/1.71  tff(99,plain,
% 1.53/1.71      (((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))) <=> ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))))),
% 1.53/1.71      inference(monotonicity,[status(thm)],[98])).
% 1.53/1.71  tff(100,plain,
% 1.53/1.71      (((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))) <=> ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) | (~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))))),
% 1.53/1.71      inference(transitivity,[status(thm)],[99, 97])).
% 1.53/1.71  tff(101,plain,
% 1.53/1.71      ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))),
% 1.53/1.71      inference(quant_inst,[status(thm)],[])).
% 1.53/1.71  tff(102,plain,
% 1.53/1.71      ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V0s))) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, V0s, A_27a!3)), V1t)))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), V0s), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s))))))))))) | (~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))),
% 1.53/1.71      inference(modus_ponens,[status(thm)],[101, 100])).
% 1.53/1.71  tff(103,plain,
% 1.53/1.71      ((~mem(ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), arr(A_27a!3, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))),
% 1.53/1.71      inference(unit_resolution,[status(thm)],[102, 96])).
% 1.53/1.71  tff(104,plain,
% 1.53/1.71      (![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))),
% 1.53/1.71      inference(unit_resolution,[status(thm)],[103, 70])).
% 1.53/1.71  tff(105,plain,
% 1.53/1.71      (((~![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)))))))))) <=> ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))) | (~mem(V0s!4, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)))))))))),
% 1.53/1.71      inference(rewrite,[status(thm)],[])).
% 1.53/1.71  tff(106,plain,
% 1.53/1.71      (((~mem(V0s!4, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))))))) <=> ((~mem(V0s!4, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)))))))))),
% 1.53/1.71      inference(rewrite,[status(thm)],[])).
% 1.53/1.71  tff(107,plain,
% 1.53/1.71      (((~![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))) <=> ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))))))))))),
% 1.53/1.71      inference(monotonicity,[status(thm)],[106])).
% 1.53/1.71  tff(108,plain,
% 1.53/1.71      (((~![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))) <=> ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))) | (~mem(V0s!4, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)))))))))),
% 1.53/1.71      inference(transitivity,[status(thm)],[107, 105])).
% 1.53/1.71  tff(109,plain,
% 1.53/1.71      ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))),
% 1.53/1.72      inference(quant_inst,[status(thm)],[])).
% 1.53/1.72  tff(110,plain,
% 1.53/1.72      ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))))))))))) | (~mem(V0s!4, arr(A_27a!3, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))))))))),
% 1.53/1.72      inference(modus_ponens,[status(thm)],[109, 108])).
% 1.53/1.72  tff(111,plain,
% 1.53/1.72      (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)))))))),
% 1.53/1.72      inference(unit_resolution,[status(thm)],[110, 27, 104])).
% 1.53/1.72  tff(112,plain,
% 1.53/1.72      (((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))) | ![V2x: $i] : ((~mem(V2x, A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), V0s!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V2x), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4))))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))))))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)))))),
% 1.53/1.72      inference(tautology,[status(thm)],[])).
% 1.53/1.72  tff(113,plain,
% 1.53/1.72      (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))))),
% 1.53/1.72      inference(unit_resolution,[status(thm)],[112, 111])).
% 1.53/1.72  tff(114,plain,
% 1.53/1.72      (~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4))),
% 1.53/1.72      inference(or_elim,[status(thm)],[26])).
% 1.53/1.72  tff(115,plain,
% 1.53/1.72      ((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)))))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))))),
% 1.53/1.72      inference(tautology,[status(thm)],[])).
% 1.53/1.72  tff(116,plain,
% 1.53/1.72      ((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!3), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)), V0s!4)) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)))))) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))))),
% 1.53/1.72      inference(unit_resolution,[status(thm)],[115, 114])).
% 1.53/1.72  tff(117,plain,
% 1.53/1.72      (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)))),
% 1.53/1.72      inference(unit_resolution,[status(thm)],[116, 113])).
% 1.53/1.72  tff(118,plain,
% 1.53/1.72      (((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))),
% 1.53/1.72      inference(tautology,[status(thm)],[])).
% 1.53/1.72  tff(119,plain,
% 1.53/1.72      (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))),
% 1.53/1.72      inference(unit_resolution,[status(thm)],[118, 117])).
% 1.53/1.72  tff(120,plain,
% 1.53/1.72      (p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))),
% 1.53/1.72      inference(modus_ponens,[status(thm)],[119, 35])).
% 1.53/1.72  tff(121,plain,
% 1.53/1.72      (((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)),
% 1.53/1.72      inference(tautology,[status(thm)],[])).
% 1.53/1.72  tff(122,plain,
% 1.53/1.72      (mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)),
% 1.53/1.72      inference(unit_resolution,[status(thm)],[121, 117])).
% 1.53/1.72  tff(123,plain,
% 1.53/1.72      (^[A_27a: $i] : refl(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))))),
% 1.53/1.72      inference(bind,[status(th)],[])).
% 1.53/1.72  tff(124,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))))),
% 1.53/1.72      inference(quant_intro,[status(thm)],[123])).
% 1.53/1.72  tff(125,plain,
% 1.53/1.72      (^[A_27a: $i] : rewrite(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))))),
% 1.53/1.72      inference(bind,[status(th)],[])).
% 1.53/1.72  tff(126,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))))),
% 1.53/1.72      inference(quant_intro,[status(thm)],[125])).
% 1.53/1.72  tff(127,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))))),
% 1.53/1.72      inference(transitivity,[status(thm)],[126, 124])).
% 1.53/1.72  tff(128,plain,
% 1.53/1.72      (^[A_27a: $i] : rewrite(((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))))))))))),
% 1.53/1.72      inference(bind,[status(th)],[])).
% 1.53/1.72  tff(129,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))))),
% 1.53/1.72      inference(quant_intro,[status(thm)],[128])).
% 1.53/1.72  tff(130,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))),
% 1.53/1.72      inference(rewrite,[status(thm)],[])).
% 1.53/1.72  tff(131,plain,
% 1.53/1.72      (^[A_27a: $i] : trans(monotonicity(quant_intro(proof_bind(^[V0s: $i] : trans(monotonicity(quant_intro(proof_bind(^[V1x: $i] : trans(monotonicity(quant_intro(proof_bind(^[V2y: $i] : rewrite((mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))) <=> ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))), (![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))) <=> ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))), ((mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))) <=> (mem(V1x, A_27a) => ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))), rewrite((mem(V1x, A_27a) => ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))) <=> ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))), ((mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))) <=> ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))), (![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))) <=> ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))), ((mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))), rewrite((mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))), ((mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))))), (![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))), ((ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> (ne(A_27a) => ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))))), rewrite((ne(A_27a) => ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))), ((ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))))),
% 1.53/1.72      inference(bind,[status(th)],[])).
% 1.53/1.72  tff(132,plain,
% 1.53/1.72      (![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))) <=> ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))),
% 1.53/1.72      inference(quant_intro,[status(thm)],[131])).
% 1.53/1.72  tff(133,axiom,(![A_27a: $i] : (ne(A_27a) => ![V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_thm_2Epred__set_2EIN__DELETE')).
% 1.53/1.72  tff(134,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))),
% 1.53/1.72      inference(modus_ponens,[status(thm)],[133, 132])).
% 1.53/1.72  tff(135,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))),
% 1.53/1.72      inference(modus_ponens,[status(thm)],[134, 130])).
% 1.53/1.72  tff(136,plain,(
% 1.53/1.72      ![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))),
% 1.53/1.72      inference(skolemize,[status(sab)],[135])).
% 1.53/1.72  tff(137,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))))),
% 1.53/1.72      inference(modus_ponens,[status(thm)],[136, 129])).
% 1.53/1.72  tff(138,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))))),
% 1.53/1.72      inference(modus_ponens,[status(thm)],[137, 127])).
% 1.53/1.72  tff(139,plain,
% 1.53/1.72      (((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y)))))))))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y)))))))))),
% 1.53/1.72      inference(rewrite,[status(thm)],[])).
% 1.53/1.72  tff(140,plain,
% 1.53/1.72      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))))) | ((~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y)))))))))),
% 1.53/1.72      inference(quant_inst,[status(thm)],[])).
% 1.53/1.72  tff(141,plain,
% 1.53/1.72      ((~![A_27a: $i] : ((~ne(A_27a)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y)))))))))) | (~ne(A_27a!3)) | ![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))))))))),
% 1.53/1.72      inference(modus_ponens,[status(thm)],[140, 139])).
% 1.53/1.72  tff(142,plain,
% 1.53/1.72      (![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))))))))),
% 1.53/1.72      inference(unit_resolution,[status(thm)],[141, 138, 8])).
% 1.53/1.72  tff(143,plain,
% 1.53/1.72      (((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))))))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))))))))) <=> ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))))))))) | (~mem(V0s!4, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))))))))),
% 1.53/1.72      inference(rewrite,[status(thm)],[])).
% 1.53/1.72  tff(144,plain,
% 1.53/1.72      ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))))))))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))))))))),
% 1.53/1.72      inference(quant_inst,[status(thm)],[])).
% 1.53/1.72  tff(145,plain,
% 1.53/1.72      ((~![V0s: $i] : ((~mem(V0s, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s), V2y))))))))) | (~mem(V0s!4, arr(A_27a!3, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y)))))))),
% 1.53/1.72      inference(modus_ponens,[status(thm)],[144, 143])).
% 1.53/1.72  tff(146,plain,
% 1.53/1.72      (![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y)))))))),
% 1.53/1.72      inference(unit_resolution,[status(thm)],[145, 27, 142])).
% 1.53/1.72  tff(147,plain,
% 1.53/1.72      (((~![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y)))))))) | ((~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y)))))))) <=> ((~![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y)))))))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y)))))))),
% 1.53/1.72      inference(rewrite,[status(thm)],[])).
% 1.53/1.72  tff(148,plain,
% 1.53/1.72      ((~![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y)))))))) | ((~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y)))))))),
% 1.53/1.72      inference(quant_inst,[status(thm)],[])).
% 1.53/1.72  tff(149,plain,
% 1.53/1.72      ((~![V1x: $i] : ((~mem(V1x, A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), V0s!4))) | (V1x = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y)))))))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | ![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))))))),
% 1.53/1.72      inference(modus_ponens,[status(thm)],[148, 147])).
% 1.53/1.72  tff(150,plain,
% 1.53/1.72      (![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))))))),
% 1.53/1.72      inference(unit_resolution,[status(thm)],[149, 146, 122])).
% 1.53/1.72  tff(151,plain,
% 1.53/1.72      (^[A_27a: $i] : refl(((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))) <=> ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))))),
% 1.53/1.72      inference(bind,[status(th)],[])).
% 1.53/1.72  tff(152,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))) <=> ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.53/1.72      inference(quant_intro,[status(thm)],[151])).
% 1.53/1.72  tff(153,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))) <=> ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.53/1.72      inference(rewrite,[status(thm)],[])).
% 1.53/1.72  tff(154,plain,
% 1.53/1.72      (^[A_27a: $i] : rewrite((ne(A_27a) => mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))) <=> ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))))),
% 1.53/1.72      inference(bind,[status(th)],[])).
% 1.53/1.72  tff(155,plain,
% 1.53/1.72      (![A_27a: $i] : (ne(A_27a) => mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))) <=> ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.53/1.72      inference(quant_intro,[status(thm)],[154])).
% 1.53/1.72  tff(156,axiom,(![A_27a: $i] : (ne(A_27a) => mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mem_c_2Epred__set_2ECHOICE')).
% 1.53/1.72  tff(157,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.53/1.72      inference(modus_ponens,[status(thm)],[156, 155])).
% 1.53/1.72  tff(158,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.53/1.72      inference(modus_ponens,[status(thm)],[157, 153])).
% 1.53/1.72  tff(159,plain,(
% 1.53/1.72      ![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.53/1.72      inference(skolemize,[status(sab)],[158])).
% 1.53/1.72  tff(160,plain,
% 1.53/1.72      (![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 1.53/1.72      inference(modus_ponens,[status(thm)],[159, 152])).
% 1.53/1.72  tff(161,plain,
% 1.53/1.72      (((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))) | ((~ne(A_27a!3)) | mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3)))) <=> ((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))) | (~ne(A_27a!3)) | mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3)))),
% 1.53/1.73      inference(rewrite,[status(thm)],[])).
% 1.53/1.73  tff(162,plain,
% 1.53/1.73      ((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))) | ((~ne(A_27a!3)) | mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3)))),
% 1.53/1.73      inference(quant_inst,[status(thm)],[])).
% 1.53/1.73  tff(163,plain,
% 1.53/1.73      ((~![A_27a: $i] : ((~ne(A_27a)) | mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))) | (~ne(A_27a!3)) | mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3))),
% 1.53/1.73      inference(modus_ponens,[status(thm)],[162, 161])).
% 1.53/1.73  tff(164,plain,
% 1.53/1.73      (mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3))),
% 1.53/1.73      inference(unit_resolution,[status(thm)],[163, 160, 8])).
% 1.53/1.73  tff(165,plain,
% 1.53/1.73      (((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3)))) <=> ((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3)))),
% 1.53/1.73      inference(rewrite,[status(thm)],[])).
% 1.53/1.73  tff(166,plain,
% 1.53/1.73      ((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3)))),
% 1.53/1.73      inference(quant_inst,[status(thm)],[])).
% 1.53/1.73  tff(167,plain,
% 1.53/1.73      ((~![A: $i, B: $i, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2ECHOICE(A_27a!3), arr(arr(A_27a!3, bool), A_27a!3))) | ![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3))),
% 1.53/1.73      inference(modus_ponens,[status(thm)],[166, 165])).
% 1.53/1.73  tff(168,plain,
% 1.53/1.73      (![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3))),
% 1.53/1.73      inference(unit_resolution,[status(thm)],[167, 62, 164])).
% 1.53/1.73  tff(169,plain,
% 1.53/1.73      (((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3))) <=> ((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3))) | (~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3))),
% 1.53/1.73      inference(rewrite,[status(thm)],[])).
% 1.53/1.73  tff(170,plain,
% 1.53/1.73      ((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3))) | ((~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3))),
% 1.53/1.73      inference(quant_inst,[status(thm)],[])).
% 1.53/1.73  tff(171,plain,
% 1.53/1.73      ((~![X: $i] : ((~mem(X, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), X), A_27a!3))) | (~mem(V0s!4, arr(A_27a!3, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3)),
% 1.53/1.73      inference(modus_ponens,[status(thm)],[170, 169])).
% 1.53/1.73  tff(172,plain,
% 1.53/1.73      (mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3)),
% 1.53/1.73      inference(unit_resolution,[status(thm)],[171, 27, 168])).
% 1.53/1.73  tff(173,plain,
% 1.53/1.73      (((~![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))))))) | ((~mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))))))) <=> ((~![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))))))) | (~mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))))))),
% 1.53/1.73      inference(rewrite,[status(thm)],[])).
% 1.53/1.73  tff(174,plain,
% 1.53/1.73      ((~![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))))))) | ((~mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))))))),
% 1.53/1.73      inference(quant_inst,[status(thm)],[])).
% 1.53/1.73  tff(175,plain,
% 1.53/1.73      ((~![V2y: $i] : ((~mem(V2y, A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = V2y)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), V2y))))))) | (~mem(ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4), A_27a!3)) | (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))))),
% 1.53/1.73      inference(modus_ponens,[status(thm)],[174, 173])).
% 1.53/1.73  tff(176,plain,
% 1.53/1.73      (~(((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))))),
% 1.53/1.73      inference(unit_resolution,[status(thm)],[175, 172, 150])).
% 1.53/1.73  tff(177,plain,
% 1.53/1.73      (((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(c_2Epred__set_2EREST(A_27a!3), V0s!4)))) | (~mem(tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3), A_27a!3)) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4)))),
% 1.53/1.74      inference(tautology,[status(thm)],[])).
% 1.53/1.74  tff(178,plain,
% 1.53/1.74      (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))),
% 1.53/1.74      inference(unit_resolution,[status(thm)],[177, 117])).
% 1.53/1.74  tff(179,plain,
% 1.53/1.74      (((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))) | p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))),
% 1.53/1.74      inference(tautology,[status(thm)],[])).
% 1.53/1.74  tff(180,plain,
% 1.53/1.74      ((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))),
% 1.53/1.74      inference(unit_resolution,[status(thm)],[179, 178])).
% 1.53/1.74  tff(181,plain,
% 1.53/1.74      ((((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))))),
% 1.53/1.74      inference(tautology,[status(thm)],[])).
% 1.53/1.74  tff(182,plain,
% 1.53/1.74      ((((~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), V0s!4))) | (tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3) = ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4)))))),
% 1.53/1.74      inference(unit_resolution,[status(thm)],[181, 180])).
% 1.53/1.74  tff(183,plain,
% 1.53/1.74      (~p(ap(ap(c_2Ebool_2EIN(A_27a!3), tptp_fun_V2x_2(V0s!4, ap(c_2Epred__set_2EREST(A_27a!3), V0s!4), A_27a!3)), ap(ap(c_2Epred__set_2EDELETE(A_27a!3), V0s!4), ap(c_2Epred__set_2ECHOICE(A_27a!3), V0s!4))))),
% 1.53/1.74      inference(unit_resolution,[status(thm)],[182, 176])).
% 1.53/1.74  tff(184,plain,
% 1.53/1.74      ($false),
% 1.53/1.74      inference(unit_resolution,[status(thm)],[183, 120])).
% 1.53/1.74  % SZS output end Proof
% 1.53/1.74  % E exiting
%------------------------------------------------------------------------------