TSTP Solution File: ITP004_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP004_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 04:14:39 EDT 2022
% Result : Theorem 0.84s 0.85s
% Output : Proof 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP004_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Sep 1 02:15:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.84/0.85 % SZS status Theorem
% 0.84/0.85 % SZS output start Proof
% 0.84/0.85 tff(p_type, type, (
% 0.84/0.85 p: $i > $o)).
% 0.84/0.85 tff(ap_type, type, (
% 0.84/0.85 ap: ( $i * $i ) > $i)).
% 0.84/0.85 tff(tptp_fun_V0s_3_type, type, (
% 0.84/0.85 tptp_fun_V0s_3: $i)).
% 0.84/0.85 tff(c_2Epred__set_2ECHOICE_type, type, (
% 0.84/0.85 c_2Epred__set_2ECHOICE: del > $i)).
% 0.84/0.85 tff(tptp_fun_A_27a_4_type, type, (
% 0.84/0.85 tptp_fun_A_27a_4: del)).
% 0.84/0.85 tff(c_2Epred__set_2EDELETE_type, type, (
% 0.84/0.85 c_2Epred__set_2EDELETE: del > $i)).
% 0.84/0.85 tff(tptp_fun_V2x_2_type, type, (
% 0.84/0.85 tptp_fun_V2x_2: ( $i * $i * del ) > $i)).
% 0.84/0.85 tff(c_2Epred__set_2EREST_type, type, (
% 0.84/0.85 c_2Epred__set_2EREST: del > $i)).
% 0.84/0.85 tff(c_2Ebool_2EIN_type, type, (
% 0.84/0.85 c_2Ebool_2EIN: del > $i)).
% 0.84/0.85 tff(mem_type, type, (
% 0.84/0.85 mem: ( $i * del ) > $o)).
% 0.84/0.85 tff(arr_type, type, (
% 0.84/0.85 arr: ( del * del ) > del)).
% 0.84/0.85 tff(bool_type, type, (
% 0.84/0.85 bool: del)).
% 0.84/0.85 tff(c_2Epred__set_2ESUBSET_type, type, (
% 0.84/0.85 c_2Epred__set_2ESUBSET: del > $i)).
% 0.84/0.85 tff(1,plain,
% 0.84/0.85 ((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))) <=> (~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(2,plain,
% 0.84/0.85 ((~![A_27a: del, V0s: $i] : (mem(V0s, arr(A_27a, bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))) <=> (~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s))))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(3,axiom,(~![A_27a: del, V0s: $i] : (mem(V0s, arr(A_27a, bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_thm_2Epred__set_2EREST__SUBSET')).
% 0.84/0.85 tff(4,plain,
% 0.84/0.85 (~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.84/0.85 tff(5,plain,
% 0.84/0.85 (~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.84/0.85 tff(6,plain,
% 0.84/0.85 (~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.84/0.85 tff(7,plain,
% 0.84/0.85 (~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.84/0.85 tff(8,plain,
% 0.84/0.85 (~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.84/0.85 tff(9,plain,
% 0.84/0.85 (~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.84/0.85 tff(10,plain,
% 0.84/0.85 (~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), ap(c_2Epred__set_2EREST(A_27a), V0s)), V0s)))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.84/0.85 tff(11,plain,(
% 0.84/0.85 ~((~mem(V0s!3, arr(A_27a!4, bool))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)))),
% 0.84/0.85 inference(skolemize,[status(sab)],[10])).
% 0.84/0.85 tff(12,plain,
% 0.84/0.85 (mem(V0s!3, arr(A_27a!4, bool))),
% 0.84/0.85 inference(or_elim,[status(thm)],[11])).
% 0.84/0.85 tff(13,plain,
% 0.84/0.85 (^[A_27a: del, V0s: $i] : refl(((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))) <=> ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 0.84/0.85 inference(bind,[status(th)],[])).
% 0.84/0.85 tff(14,plain,
% 0.84/0.85 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))),
% 0.84/0.85 inference(quant_intro,[status(thm)],[13])).
% 0.84/0.85 tff(15,plain,
% 0.84/0.85 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(16,plain,
% 0.84/0.85 (^[A_27a: del, V0s: $i] : rewrite((mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))) <=> ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))))),
% 0.84/0.85 inference(bind,[status(th)],[])).
% 0.84/0.85 tff(17,plain,
% 0.84/0.85 (![A_27a: del, V0s: $i] : (mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s)))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))),
% 0.84/0.85 inference(quant_intro,[status(thm)],[16])).
% 0.84/0.85 tff(18,axiom,(![A_27a: del, V0s: $i] : (mem(V0s, arr(A_27a, bool)) => (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax_thm_2Epred__set_2EREST__DEF')).
% 0.84/0.85 tff(19,plain,
% 0.84/0.85 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.84/0.85 tff(20,plain,
% 0.84/0.85 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.84/0.85 tff(21,plain,(
% 0.84/0.85 ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))),
% 0.84/0.85 inference(skolemize,[status(sab)],[20])).
% 0.84/0.85 tff(22,plain,
% 0.84/0.85 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.84/0.85 tff(23,plain,
% 0.84/0.85 (((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | (ap(c_2Epred__set_2EREST(A_27a!4), V0s!3) = ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))) <=> ((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) | (~mem(V0s!3, arr(A_27a!4, bool))) | (ap(c_2Epred__set_2EREST(A_27a!4), V0s!3) = ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(24,plain,
% 0.84/0.85 ((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | (ap(c_2Epred__set_2EREST(A_27a!4), V0s!3) = ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))),
% 0.84/0.86 inference(quant_inst,[status(thm)],[])).
% 0.84/0.86 tff(25,plain,
% 0.84/0.86 ((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | (ap(c_2Epred__set_2EREST(A_27a), V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), ap(c_2Epred__set_2ECHOICE(A_27a), V0s))))) | (~mem(V0s!3, arr(A_27a!4, bool))) | (ap(c_2Epred__set_2EREST(A_27a!4), V0s!3) = ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.84/0.86 tff(26,plain,
% 0.84/0.86 (ap(c_2Epred__set_2EREST(A_27a!4), V0s!3) = ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))),
% 0.84/0.86 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.84/0.86 tff(27,plain,
% 0.84/0.86 (ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)) = ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)),
% 0.84/0.86 inference(symmetry,[status(thm)],[26])).
% 0.84/0.86 tff(28,plain,
% 0.84/0.86 (ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))) = ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))),
% 0.84/0.86 inference(monotonicity,[status(thm)],[27])).
% 0.84/0.86 tff(29,plain,
% 0.84/0.86 (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))),
% 0.84/0.86 inference(monotonicity,[status(thm)],[28])).
% 0.84/0.86 tff(30,plain,
% 0.84/0.86 (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))),
% 0.84/0.86 inference(symmetry,[status(thm)],[29])).
% 0.84/0.86 tff(31,plain,
% 0.84/0.86 (^[A_27a: del] : refl(mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))) <=> mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))))),
% 0.84/0.86 inference(bind,[status(th)],[])).
% 0.84/0.86 tff(32,plain,
% 0.84/0.86 (![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))) <=> ![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))),
% 0.84/0.86 inference(quant_intro,[status(thm)],[31])).
% 0.84/0.86 tff(33,plain,
% 0.84/0.86 (![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool))) <=> ![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))),
% 0.84/0.86 inference(rewrite,[status(thm)],[])).
% 0.84/0.86 tff(34,axiom,(![A_27a: del] : 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')).
% 0.84/0.86 tff(35,plain,
% 0.84/0.86 (![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.84/0.86 tff(36,plain,(
% 0.84/0.86 ![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))),
% 0.84/0.86 inference(skolemize,[status(sab)],[35])).
% 0.84/0.86 tff(37,plain,
% 0.84/0.86 (![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.84/0.86 tff(38,plain,
% 0.84/0.86 ((~![A_27a: del] : mem(c_2Epred__set_2EREST(A_27a), arr(arr(A_27a, bool), arr(A_27a, bool)))) | mem(c_2Epred__set_2EREST(A_27a!4), arr(arr(A_27a!4, bool), arr(A_27a!4, bool)))),
% 0.84/0.86 inference(quant_inst,[status(thm)],[])).
% 0.84/0.86 tff(39,plain,
% 0.84/0.86 (mem(c_2Epred__set_2EREST(A_27a!4), arr(arr(A_27a!4, bool), arr(A_27a!4, bool)))),
% 0.84/0.86 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.84/0.86 tff(40,plain,
% 0.84/0.86 (^[A: del, B: del, F: $i] : refl(((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(41,plain,
% 0.98/0.86 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[40])).
% 0.98/0.86 tff(42,plain,
% 0.98/0.86 (^[A: del, B: del, F: $i] : rewrite(((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(43,plain,
% 0.98/0.86 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[42])).
% 0.98/0.86 tff(44,plain,
% 0.98/0.86 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 0.98/0.86 inference(transitivity,[status(thm)],[43, 41])).
% 0.98/0.86 tff(45,plain,
% 0.98/0.86 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(46,plain,
% 0.98/0.86 (^[A: del, B: del, F: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite((mem(X, A) => mem(ap(F, X), B)) <=> ((~mem(X, A)) | mem(ap(F, X), B)))), (![X: $i] : (mem(X, A) => mem(ap(F, X), B)) <=> ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))), ((mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> (mem(F, arr(A, B)) => ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))), rewrite((mem(F, arr(A, B)) => ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))), ((mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(47,plain,
% 0.98/0.86 (![A: del, B: del, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[46])).
% 0.98/0.86 tff(48,axiom,(![A: del, B: del, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B)))), file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001_2.ax','ap_tp')).
% 0.98/0.86 tff(49,plain,
% 0.98/0.86 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.98/0.86 tff(50,plain,
% 0.98/0.86 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.98/0.86 tff(51,plain,(
% 0.98/0.86 ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 0.98/0.86 inference(skolemize,[status(sab)],[50])).
% 0.98/0.86 tff(52,plain,
% 0.98/0.86 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.98/0.86 tff(53,plain,
% 0.98/0.86 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2EREST(A_27a!4), arr(arr(A_27a!4, bool), arr(A_27a!4, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool))))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2EREST(A_27a!4), arr(arr(A_27a!4, bool), arr(A_27a!4, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(54,plain,
% 0.98/0.86 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2EREST(A_27a!4), arr(arr(A_27a!4, bool), arr(A_27a!4, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool))))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(55,plain,
% 0.98/0.86 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2EREST(A_27a!4), arr(arr(A_27a!4, bool), arr(A_27a!4, bool)))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.98/0.86 tff(56,plain,
% 0.98/0.86 (![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool)))),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[55, 52, 39])).
% 0.98/0.86 tff(57,plain,
% 0.98/0.86 (((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool)))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool)))) <=> ((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool)))) | (~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(58,plain,
% 0.98/0.86 ((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool)))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool)))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(59,plain,
% 0.98/0.86 ((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), X), arr(A_27a!4, bool)))) | (~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.98/0.86 tff(60,plain,
% 0.98/0.86 (mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[59, 12, 56])).
% 0.98/0.86 tff(61,plain,
% 0.98/0.86 (^[A_27a: del, V0s: $i] : rewrite(((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(62,plain,
% 0.98/0.86 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[61])).
% 0.98/0.86 tff(63,plain,
% 0.98/0.86 (^[A_27a: del, V0s: $i] : refl(((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(64,plain,
% 0.98/0.86 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[63])).
% 0.98/0.86 tff(65,plain,
% 0.98/0.86 (^[A_27a: del, V0s: $i] : rewrite(((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(66,plain,
% 0.98/0.86 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[65])).
% 0.98/0.86 tff(67,plain,
% 0.98/0.86 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))),
% 0.98/0.86 inference(transitivity,[status(thm)],[66, 64])).
% 0.98/0.86 tff(68,plain,
% 0.98/0.86 (^[A_27a: del, V0s: $i] : rewrite(((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))) & (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(69,plain,
% 0.98/0.86 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))) & (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[68])).
% 0.98/0.86 tff(70,plain,
% 0.98/0.86 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(71,plain,
% 0.98/0.86 (^[A_27a: del, V0s: $i] : trans(monotonicity(quant_intro(proof_bind(^[V1t: $i] : trans(monotonicity(rewrite((p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))) <=> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))), ((mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))) <=> (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))), rewrite((mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) <=> ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))), ((mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))) <=> ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))), (![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))) <=> ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))), ((mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))))) <=> (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))), rewrite((mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))), ((mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(72,plain,
% 0.98/0.86 (![A_27a: del, V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t))))))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[71])).
% 0.98/0.86 tff(73,axiom,(![A_27a: del, V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1t: $i] : (mem(V1t, arr(A_27a, bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (mem(V2x, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax_thm_2Epred__set_2ESUBSET__DEF')).
% 0.98/0.86 tff(74,plain,
% 0.98/0.86 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.98/0.86 tff(75,plain,
% 0.98/0.86 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) <=> ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.98/0.86 tff(76,plain,(
% 0.98/0.86 ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))) & (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))),
% 0.98/0.86 inference(skolemize,[status(sab)],[75])).
% 0.98/0.86 tff(77,plain,
% 0.98/0.86 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.98/0.86 tff(78,plain,
% 0.98/0.86 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s)))))) | (~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s)))))))))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.98/0.86 tff(79,plain,
% 0.98/0.86 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[78, 62])).
% 0.98/0.86 tff(80,plain,
% 0.98/0.86 (((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))) <=> ((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))) | (~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(81,plain,
% 0.98/0.86 (((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~mem(V2x, A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) <=> ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(82,plain,
% 0.98/0.87 (((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~mem(V2x, A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))) <=> ((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))))),
% 0.98/0.87 inference(monotonicity,[status(thm)],[81])).
% 0.98/0.87 tff(83,plain,
% 0.98/0.87 (((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~mem(V2x, A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))) <=> ((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))) | (~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))),
% 0.98/0.87 inference(transitivity,[status(thm)],[82, 80])).
% 0.98/0.87 tff(84,plain,
% 0.98/0.87 ((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))) | ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~mem(V2x, A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(85,plain,
% 0.98/0.87 ((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, V0s, A_27a), A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), tptp_fun_V2x_2(V1t, V0s, A_27a)), V0s))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a), V0s), V1t))) | ![V2x: $i] : (p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V1t)) | (~mem(V2x, A_27a)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a), V2x), V0s))))))))))) | (~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.98/0.87 tff(86,plain,
% 0.98/0.87 ((~mem(ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), arr(A_27a!4, bool))) | ![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[85, 79])).
% 0.98/0.87 tff(87,plain,
% 0.98/0.87 (![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[86, 60])).
% 0.98/0.87 tff(88,plain,
% 0.98/0.87 (((~![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) <=> ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) | (~mem(V0s!3, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(89,plain,
% 0.98/0.87 ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(90,plain,
% 0.98/0.87 ((~![V1t: $i] : ((~mem(V1t, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V1t)) | (~mem(tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V1t, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V1t))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V1t)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))))) | (~mem(V0s!3, arr(A_27a!4, bool))) | (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.98/0.87 tff(91,plain,
% 0.98/0.87 (~((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[90, 12, 87])).
% 0.98/0.87 tff(92,plain,
% 0.98/0.87 (((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~((~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))) | ![V2x: $i] : ((~mem(V2x, A_27a!4)) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), V0s!3)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V2x), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))),
% 0.98/0.87 inference(tautology,[status(thm)],[])).
% 0.98/0.87 tff(93,plain,
% 0.98/0.87 (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.98/0.87 tff(94,plain,
% 0.98/0.87 (~p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3))),
% 0.98/0.87 inference(or_elim,[status(thm)],[11])).
% 0.98/0.87 tff(95,plain,
% 0.98/0.87 ((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))),
% 0.98/0.87 inference(tautology,[status(thm)],[])).
% 0.98/0.87 tff(96,plain,
% 0.98/0.87 ((~(p(ap(ap(c_2Epred__set_2ESUBSET(A_27a!4), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)), V0s!3)) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))))) | (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.98/0.87 tff(97,plain,
% 0.98/0.87 (~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[96, 93])).
% 0.98/0.87 tff(98,plain,
% 0.98/0.87 ((p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))),
% 0.98/0.87 inference(tautology,[status(thm)],[])).
% 0.98/0.87 tff(99,plain,
% 0.98/0.87 (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3)))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.98/0.87 tff(100,plain,
% 0.98/0.87 (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[99, 30])).
% 0.98/0.88 tff(101,plain,
% 0.98/0.88 ((p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))) | mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)),
% 0.98/0.88 inference(tautology,[status(thm)],[])).
% 0.98/0.88 tff(102,plain,
% 0.98/0.88 (mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[101, 97])).
% 0.98/0.88 tff(103,plain,
% 0.98/0.88 (^[A_27a: del, V0s: $i] : refl(((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), 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))))))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(104,plain,
% 0.98/0.88 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[103])).
% 0.98/0.88 tff(105,plain,
% 0.98/0.88 (^[A_27a: del, V0s: $i] : rewrite(((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(106,plain,
% 0.98/0.88 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[105])).
% 0.98/0.88 tff(107,plain,
% 0.98/0.88 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))),
% 0.98/0.88 inference(transitivity,[status(thm)],[106, 104])).
% 0.98/0.88 tff(108,plain,
% 0.98/0.88 (^[A_27a: del, V0s: $i] : rewrite(((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y))))))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(109,plain,
% 0.98/0.88 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[108])).
% 0.98/0.88 tff(110,plain,
% 0.98/0.88 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(111,plain,
% 0.98/0.88 (^[A_27a: del, V0s: $i] : trans(monotonicity(quant_intro(proof_bind(^[V1x: $i] : trans(monotonicity(quant_intro(proof_bind(^[V2y: $i] : rewrite((mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))) <=> ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))), (![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))) <=> ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))), ((mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))) <=> (mem(V1x, A_27a) => ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))), rewrite((mem(V1x, A_27a) => ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))) <=> ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))), ((mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))) <=> ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))), (![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))) <=> ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))), ((mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))))), rewrite((mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))), ((mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(112,plain,
% 0.98/0.88 (![A_27a: del, V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y))))))) <=> ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[111])).
% 0.98/0.88 tff(113,axiom,(![A_27a: del, V0s: $i] : (mem(V0s, arr(A_27a, bool)) => ![V1x: $i] : (mem(V1x, A_27a) => ![V2y: $i] : (mem(V2y, A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_thm_2Epred__set_2EIN__DELETE')).
% 0.98/0.88 tff(114,plain,
% 0.98/0.88 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.98/0.88 tff(115,plain,
% 0.98/0.88 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.98/0.88 tff(116,plain,(
% 0.98/0.88 ![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s)) & (~(V1x = V2y)))))))),
% 0.98/0.88 inference(skolemize,[status(sab)],[115])).
% 0.98/0.88 tff(117,plain,
% 0.98/0.88 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.98/0.88 tff(118,plain,
% 0.98/0.88 (![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[117, 107])).
% 0.98/0.88 tff(119,plain,
% 0.98/0.88 (((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y)))))))) <=> ((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))) | (~mem(V0s!3, arr(A_27a!4, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y)))))))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(120,plain,
% 0.98/0.88 ((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y)))))))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(121,plain,
% 0.98/0.88 ((~![A_27a: del, V0s: $i] : ((~mem(V0s, arr(A_27a, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a)) | ![V2y: $i] : ((~mem(V2y, A_27a)) | (p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a), V0s), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a), V1x), V0s))) | (V1x = V2y)))))))) | (~mem(V0s!3, arr(A_27a!4, bool))) | ![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y))))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.98/0.88 tff(122,plain,
% 0.98/0.88 (![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y))))))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[121, 118, 12])).
% 0.98/0.88 tff(123,plain,
% 0.98/0.88 (((~![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y))))))) | ((~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y))))))) <=> ((~![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y))))))) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y))))))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(124,plain,
% 0.98/0.88 ((~![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y))))))) | ((~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y))))))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(125,plain,
% 0.98/0.88 ((~![V1x: $i] : ((~mem(V1x, A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), V1x), V0s!3))) | (V1x = V2y))))))) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | ![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.98/0.88 tff(126,plain,
% 0.98/0.88 (![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)))))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[125, 122, 102])).
% 0.98/0.88 tff(127,plain,
% 0.98/0.88 (^[A_27a: del] : refl(mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)) <=> mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(128,plain,
% 0.98/0.88 (![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)) <=> ![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[127])).
% 0.98/0.88 tff(129,plain,
% 0.98/0.88 (![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a)) <=> ![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(130,axiom,(![A_27a: del] : 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')).
% 0.98/0.88 tff(131,plain,
% 0.98/0.88 (![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.98/0.88 tff(132,plain,(
% 0.98/0.88 ![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))),
% 0.98/0.88 inference(skolemize,[status(sab)],[131])).
% 0.98/0.88 tff(133,plain,
% 0.98/0.88 (![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.98/0.88 tff(134,plain,
% 0.98/0.88 ((~![A_27a: del] : mem(c_2Epred__set_2ECHOICE(A_27a), arr(arr(A_27a, bool), A_27a))) | mem(c_2Epred__set_2ECHOICE(A_27a!4), arr(arr(A_27a!4, bool), A_27a!4))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(135,plain,
% 0.98/0.88 (mem(c_2Epred__set_2ECHOICE(A_27a!4), arr(arr(A_27a!4, bool), A_27a!4))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.98/0.88 tff(136,plain,
% 0.98/0.88 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2ECHOICE(A_27a!4), arr(arr(A_27a!4, bool), A_27a!4))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4)))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2ECHOICE(A_27a!4), arr(arr(A_27a!4, bool), A_27a!4))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(137,plain,
% 0.98/0.88 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epred__set_2ECHOICE(A_27a!4), arr(arr(A_27a!4, bool), A_27a!4))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4)))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(138,plain,
% 0.98/0.88 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epred__set_2ECHOICE(A_27a!4), arr(arr(A_27a!4, bool), A_27a!4))) | ![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.98/0.88 tff(139,plain,
% 0.98/0.88 (![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[138, 52, 135])).
% 0.98/0.88 tff(140,plain,
% 0.98/0.88 (((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4))) <=> ((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4))) | (~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(141,plain,
% 0.98/0.88 ((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4))) | ((~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(142,plain,
% 0.98/0.88 ((~![X: $i] : ((~mem(X, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), X), A_27a!4))) | (~mem(V0s!3, arr(A_27a!4, bool))) | mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.98/0.88 tff(143,plain,
% 0.98/0.88 (mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[142, 12, 139])).
% 0.98/0.88 tff(144,plain,
% 0.98/0.88 (((~![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)))))) | ((~mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))))) <=> ((~![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)))))) | (~mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(145,plain,
% 0.98/0.89 ((~![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)))))) | ((~mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(146,plain,
% 0.98/0.89 ((~![V2y: $i] : ((~mem(V2y, A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), V2y))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = V2y)))))) | (~mem(ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3), A_27a!4)) | (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.98/0.89 tff(147,plain,
% 0.98/0.89 (p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[146, 143, 126])).
% 0.98/0.89 tff(148,plain,
% 0.98/0.89 ((p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)) | (~mem(tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4), A_27a!4)) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(c_2Epred__set_2EREST(A_27a!4), V0s!3))))) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3)))),
% 1.01/0.89 inference(tautology,[status(thm)],[])).
% 1.01/0.89 tff(149,plain,
% 1.01/0.89 (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[148, 97])).
% 1.01/0.89 tff(150,plain,
% 1.01/0.89 (((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))) | p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))),
% 1.01/0.89 inference(tautology,[status(thm)],[])).
% 1.01/0.89 tff(151,plain,
% 1.01/0.89 ((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[150, 149])).
% 1.01/0.89 tff(152,plain,
% 1.01/0.89 ((~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))))) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))) | (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))),
% 1.01/0.89 inference(tautology,[status(thm)],[])).
% 1.01/0.89 tff(153,plain,
% 1.01/0.89 ((~(p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))) <=> (~((~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), V0s!3))) | (tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4) = ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))))) | (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3)))))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[152, 151])).
% 1.01/0.89 tff(154,plain,
% 1.01/0.89 (~p(ap(ap(c_2Ebool_2EIN(A_27a!4), tptp_fun_V2x_2(V0s!3, ap(c_2Epred__set_2EREST(A_27a!4), V0s!3), A_27a!4)), ap(ap(c_2Epred__set_2EDELETE(A_27a!4), V0s!3), ap(c_2Epred__set_2ECHOICE(A_27a!4), V0s!3))))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[153, 147])).
% 1.01/0.89 tff(155,plain,
% 1.01/0.89 ($false),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[154, 100])).
% 1.01/0.89 % SZS output end Proof
%------------------------------------------------------------------------------