TSTP Solution File: ITP023_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP023_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 04:15:31 EDT 2022
% Result : Theorem 1.33s 1.14s
% Output : Proof 1.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ITP023_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 03:48:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.33/1.14 % SZS status Theorem
% 1.33/1.14 % SZS output start Proof
% 1.33/1.14 tff(mem_type, type, (
% 1.33/1.14 mem: ( $i * del ) > $o)).
% 1.33/1.14 tff(arr_type, type, (
% 1.33/1.14 arr: ( del * del ) > del)).
% 1.33/1.14 tff(bool_type, type, (
% 1.33/1.14 bool: del)).
% 1.33/1.14 tff(ty_2Erealax_2Ereal_type, type, (
% 1.33/1.14 ty_2Erealax_2Ereal: del)).
% 1.33/1.14 tff(ap_type, type, (
% 1.33/1.14 ap: ( $i * $i ) > $i)).
% 1.33/1.14 tff(inj__ty_2Erealax_2Ereal_type, type, (
% 1.33/1.14 inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i)).
% 1.33/1.14 tff(tptp_fun_V1e_5_type, type, (
% 1.33/1.14 tptp_fun_V1e_5: tp__ty_2Erealax_2Ereal)).
% 1.33/1.14 tff(tptp_fun_V0x_6_type, type, (
% 1.33/1.14 tptp_fun_V0x_6: tp__ty_2Erealax_2Ereal)).
% 1.33/1.14 tff(c_2Epair_2E_2C_type, type, (
% 1.33/1.14 c_2Epair_2E_2C: ( del * del ) > $i)).
% 1.33/1.14 tff(c_2Ereal__topology_2Ecball_type, type, (
% 1.33/1.14 c_2Ereal__topology_2Ecball: $i)).
% 1.33/1.14 tff(ty_2Epair_2Eprod_type, type, (
% 1.33/1.14 ty_2Epair_2Eprod: ( del * del ) > del)).
% 1.33/1.14 tff(p_type, type, (
% 1.33/1.14 p: $i > $o)).
% 1.33/1.14 tff(c_2Ereal__topology_2Eball_type, type, (
% 1.33/1.14 c_2Ereal__topology_2Eball: $i)).
% 1.33/1.14 tff(c_2Epred__set_2ESUBSET_type, type, (
% 1.33/1.14 c_2Epred__set_2ESUBSET: del > $i)).
% 1.33/1.14 tff(c_2Ereal__topology_2Ebounded__def_type, type, (
% 1.33/1.14 c_2Ereal__topology_2Ebounded__def: $i)).
% 1.33/1.14 tff(1,plain,
% 1.33/1.14 (^[A_27a: del, A_27b: del] : refl(mem(c_2Epair_2E_2C(A_27a, A_27b), arr(A_27a, arr(A_27b, ty_2Epair_2Eprod(A_27a, A_27b)))) <=> mem(c_2Epair_2E_2C(A_27a, A_27b), arr(A_27a, arr(A_27b, ty_2Epair_2Eprod(A_27a, A_27b)))))),
% 1.33/1.14 inference(bind,[status(th)],[])).
% 1.33/1.14 tff(2,plain,
% 1.33/1.14 (![A_27a: del, A_27b: del] : mem(c_2Epair_2E_2C(A_27a, A_27b), arr(A_27a, arr(A_27b, ty_2Epair_2Eprod(A_27a, A_27b)))) <=> ![A_27a: del, A_27b: del] : mem(c_2Epair_2E_2C(A_27a, A_27b), arr(A_27a, arr(A_27b, ty_2Epair_2Eprod(A_27a, A_27b))))),
% 1.33/1.14 inference(quant_intro,[status(thm)],[1])).
% 1.33/1.14 tff(3,plain,
% 1.33/1.14 (![A_27a: del, A_27b: del] : mem(c_2Epair_2E_2C(A_27a, A_27b), arr(A_27a, arr(A_27b, ty_2Epair_2Eprod(A_27a, A_27b)))) <=> ![A_27a: del, A_27b: del] : mem(c_2Epair_2E_2C(A_27a, A_27b), arr(A_27a, arr(A_27b, ty_2Epair_2Eprod(A_27a, A_27b))))),
% 1.33/1.14 inference(rewrite,[status(thm)],[])).
% 1.33/1.14 tff(4,axiom,(![A_27a: del, A_27b: del] : mem(c_2Epair_2E_2C(A_27a, A_27b), arr(A_27a, arr(A_27b, ty_2Epair_2Eprod(A_27a, A_27b))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Epair_2E_2C')).
% 1.33/1.14 tff(5,plain,
% 1.33/1.14 (![A_27a: del, A_27b: del] : mem(c_2Epair_2E_2C(A_27a, A_27b), arr(A_27a, arr(A_27b, ty_2Epair_2Eprod(A_27a, A_27b))))),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.33/1.14 tff(6,plain,(
% 1.33/1.14 ![A_27a: del, A_27b: del] : mem(c_2Epair_2E_2C(A_27a, A_27b), arr(A_27a, arr(A_27b, ty_2Epair_2Eprod(A_27a, A_27b))))),
% 1.33/1.14 inference(skolemize,[status(sab)],[5])).
% 1.33/1.14 tff(7,plain,
% 1.33/1.14 (![A_27a: del, A_27b: del] : mem(c_2Epair_2E_2C(A_27a, A_27b), arr(A_27a, arr(A_27b, ty_2Epair_2Eprod(A_27a, A_27b))))),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.33/1.14 tff(8,plain,
% 1.33/1.14 ((~![A_27a: del, A_27b: del] : mem(c_2Epair_2E_2C(A_27a, A_27b), arr(A_27a, arr(A_27b, ty_2Epair_2Eprod(A_27a, A_27b))))) | mem(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 1.33/1.14 inference(quant_inst,[status(thm)],[])).
% 1.33/1.14 tff(9,plain,
% 1.33/1.14 (mem(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 1.33/1.14 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.33/1.14 tff(10,plain,
% 1.33/1.14 (^[A: del, B: del, F: $i] : refl(((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))),
% 1.33/1.14 inference(bind,[status(th)],[])).
% 1.33/1.14 tff(11,plain,
% 1.33/1.14 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.33/1.14 inference(quant_intro,[status(thm)],[10])).
% 1.33/1.14 tff(12,plain,
% 1.33/1.14 (^[A: del, B: del, F: $i] : rewrite(((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))),
% 1.33/1.14 inference(bind,[status(th)],[])).
% 1.33/1.14 tff(13,plain,
% 1.33/1.14 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.33/1.14 inference(quant_intro,[status(thm)],[12])).
% 1.33/1.14 tff(14,plain,
% 1.33/1.14 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.33/1.14 inference(transitivity,[status(thm)],[13, 11])).
% 1.33/1.14 tff(15,plain,
% 1.33/1.14 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.33/1.14 inference(rewrite,[status(thm)],[])).
% 1.33/1.14 tff(16,plain,
% 1.33/1.14 (^[A: del, B: del, F: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite((mem(X, A) => mem(ap(F, X), B)) <=> ((~mem(X, A)) | mem(ap(F, X), B)))), (![X: $i] : (mem(X, A) => mem(ap(F, X), B)) <=> ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))), ((mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> (mem(F, arr(A, B)) => ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))), rewrite((mem(F, arr(A, B)) => ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))), ((mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))))),
% 1.33/1.14 inference(bind,[status(th)],[])).
% 1.33/1.14 tff(17,plain,
% 1.33/1.14 (![A: del, B: del, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.33/1.14 inference(quant_intro,[status(thm)],[16])).
% 1.33/1.14 tff(18,axiom,(![A: del, B: del, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B)))), file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001_2.ax','ap_tp')).
% 1.33/1.14 tff(19,plain,
% 1.33/1.14 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.33/1.14 tff(20,plain,
% 1.33/1.14 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.33/1.14 tff(21,plain,(
% 1.33/1.14 ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.33/1.14 inference(skolemize,[status(sab)],[20])).
% 1.33/1.14 tff(22,plain,
% 1.33/1.14 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.33/1.14 tff(23,plain,
% 1.33/1.14 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))) | ![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), X), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))) | ![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), X), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))))),
% 1.33/1.14 inference(rewrite,[status(thm)],[])).
% 1.33/1.14 tff(24,plain,
% 1.33/1.14 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))) | ![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), X), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))))),
% 1.33/1.14 inference(quant_inst,[status(thm)],[])).
% 1.33/1.14 tff(25,plain,
% 1.33/1.14 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))) | ![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), X), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.33/1.14 tff(26,plain,
% 1.33/1.14 (![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), X), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 1.33/1.14 inference(unit_resolution,[status(thm)],[25, 22, 9])).
% 1.33/1.14 tff(27,plain,
% 1.33/1.14 (^[X: tp__ty_2Erealax_2Ereal] : refl(mem(inj__ty_2Erealax_2Ereal(X), ty_2Erealax_2Ereal) <=> mem(inj__ty_2Erealax_2Ereal(X), ty_2Erealax_2Ereal))),
% 1.33/1.14 inference(bind,[status(th)],[])).
% 1.33/1.14 tff(28,plain,
% 1.33/1.14 (![X: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X), ty_2Erealax_2Ereal) <=> ![X: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X), ty_2Erealax_2Ereal)),
% 1.33/1.14 inference(quant_intro,[status(thm)],[27])).
% 1.33/1.14 tff(29,plain,
% 1.33/1.14 (![X: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X), ty_2Erealax_2Ereal) <=> ![X: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X), ty_2Erealax_2Ereal)),
% 1.33/1.14 inference(rewrite,[status(thm)],[])).
% 1.33/1.14 tff(30,axiom,(![X: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X), ty_2Erealax_2Ereal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','stp_inj_mem_ty_2Erealax_2Ereal')).
% 1.33/1.14 tff(31,plain,
% 1.33/1.14 (![X: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X), ty_2Erealax_2Ereal)),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[30, 29])).
% 1.33/1.14 tff(32,plain,(
% 1.33/1.14 ![X: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X), ty_2Erealax_2Ereal)),
% 1.33/1.14 inference(skolemize,[status(sab)],[31])).
% 1.33/1.14 tff(33,plain,
% 1.33/1.14 (![X: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X), ty_2Erealax_2Ereal)),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[32, 28])).
% 1.33/1.14 tff(34,plain,
% 1.33/1.14 ((~![X: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X), ty_2Erealax_2Ereal)) | mem(inj__ty_2Erealax_2Ereal(V0x!6), ty_2Erealax_2Ereal)),
% 1.33/1.14 inference(quant_inst,[status(thm)],[])).
% 1.33/1.14 tff(35,plain,
% 1.33/1.14 (mem(inj__ty_2Erealax_2Ereal(V0x!6), ty_2Erealax_2Ereal)),
% 1.33/1.14 inference(unit_resolution,[status(thm)],[34, 33])).
% 1.33/1.14 tff(36,plain,
% 1.33/1.14 (((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), X), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))) | ((~mem(inj__ty_2Erealax_2Ereal(V0x!6), ty_2Erealax_2Ereal)) | mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))) <=> ((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), X), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))) | (~mem(inj__ty_2Erealax_2Ereal(V0x!6), ty_2Erealax_2Ereal)) | mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 1.33/1.14 inference(rewrite,[status(thm)],[])).
% 1.33/1.14 tff(37,plain,
% 1.33/1.14 ((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), X), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))) | ((~mem(inj__ty_2Erealax_2Ereal(V0x!6), ty_2Erealax_2Ereal)) | mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 1.33/1.14 inference(quant_inst,[status(thm)],[])).
% 1.33/1.14 tff(38,plain,
% 1.33/1.14 ((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), X), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))) | (~mem(inj__ty_2Erealax_2Ereal(V0x!6), ty_2Erealax_2Ereal)) | mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.33/1.14 tff(39,plain,
% 1.33/1.14 (mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))),
% 1.33/1.14 inference(unit_resolution,[status(thm)],[38, 35, 26])).
% 1.33/1.14 tff(40,plain,
% 1.33/1.14 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))) | ![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), X), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))) | ![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), X), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 1.33/1.14 inference(rewrite,[status(thm)],[])).
% 1.33/1.14 tff(41,plain,
% 1.33/1.14 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))) | ![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), X), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 1.33/1.14 inference(quant_inst,[status(thm)],[])).
% 1.33/1.14 tff(42,plain,
% 1.33/1.14 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), arr(ty_2Erealax_2Ereal, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))) | ![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), X), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.33/1.14 tff(43,plain,
% 1.33/1.14 (![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), X), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))),
% 1.33/1.14 inference(unit_resolution,[status(thm)],[42, 22, 39])).
% 1.33/1.14 tff(44,plain,
% 1.33/1.14 ((~![X: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X), ty_2Erealax_2Ereal)) | mem(inj__ty_2Erealax_2Ereal(V1e!5), ty_2Erealax_2Ereal)),
% 1.33/1.14 inference(quant_inst,[status(thm)],[])).
% 1.33/1.14 tff(45,plain,
% 1.33/1.14 (mem(inj__ty_2Erealax_2Ereal(V1e!5), ty_2Erealax_2Ereal)),
% 1.33/1.14 inference(unit_resolution,[status(thm)],[44, 33])).
% 1.33/1.14 tff(46,plain,
% 1.33/1.14 (((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), X), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))) | ((~mem(inj__ty_2Erealax_2Ereal(V1e!5), ty_2Erealax_2Ereal)) | mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))) <=> ((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), X), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))) | (~mem(inj__ty_2Erealax_2Ereal(V1e!5), ty_2Erealax_2Ereal)) | mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))),
% 1.33/1.15 inference(rewrite,[status(thm)],[])).
% 1.33/1.15 tff(47,plain,
% 1.33/1.15 ((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), X), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))) | ((~mem(inj__ty_2Erealax_2Ereal(V1e!5), ty_2Erealax_2Ereal)) | mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))),
% 1.33/1.15 inference(quant_inst,[status(thm)],[])).
% 1.33/1.15 tff(48,plain,
% 1.33/1.15 ((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), X), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))) | (~mem(inj__ty_2Erealax_2Ereal(V1e!5), ty_2Erealax_2Ereal)) | mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))),
% 1.33/1.15 inference(modus_ponens,[status(thm)],[47, 46])).
% 1.33/1.15 tff(49,plain,
% 1.33/1.15 (mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))),
% 1.33/1.15 inference(unit_resolution,[status(thm)],[48, 45, 43])).
% 1.33/1.15 tff(50,plain,
% 1.33/1.15 (mem(c_2Ereal__topology_2Ecball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool))) <=> mem(c_2Ereal__topology_2Ecball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))),
% 1.33/1.15 inference(rewrite,[status(thm)],[])).
% 1.33/1.15 tff(51,axiom,(mem(c_2Ereal__topology_2Ecball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Ereal__topology_2Ecball')).
% 1.33/1.15 tff(52,plain,
% 1.33/1.15 (mem(c_2Ereal__topology_2Ecball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))),
% 1.33/1.15 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.33/1.15 tff(53,plain,
% 1.33/1.15 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ereal__topology_2Ecball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))) | ![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, X), arr(ty_2Erealax_2Ereal, bool))))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ereal__topology_2Ecball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))) | ![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, X), arr(ty_2Erealax_2Ereal, bool))))),
% 1.33/1.15 inference(rewrite,[status(thm)],[])).
% 1.33/1.15 tff(54,plain,
% 1.33/1.15 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ereal__topology_2Ecball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))) | ![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, X), arr(ty_2Erealax_2Ereal, bool))))),
% 1.33/1.15 inference(quant_inst,[status(thm)],[])).
% 1.33/1.15 tff(55,plain,
% 1.33/1.15 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ereal__topology_2Ecball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))) | ![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, X), arr(ty_2Erealax_2Ereal, bool)))),
% 1.33/1.15 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.33/1.15 tff(56,plain,
% 1.33/1.15 (![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, X), arr(ty_2Erealax_2Ereal, bool)))),
% 1.33/1.15 inference(unit_resolution,[status(thm)],[55, 22, 52])).
% 1.33/1.15 tff(57,plain,
% 1.33/1.15 (((~![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, X), arr(ty_2Erealax_2Ereal, bool)))) | ((~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool)))) <=> ((~![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, X), arr(ty_2Erealax_2Ereal, bool)))) | (~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool)))),
% 1.33/1.15 inference(rewrite,[status(thm)],[])).
% 1.33/1.15 tff(58,plain,
% 1.33/1.15 ((~![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, X), arr(ty_2Erealax_2Ereal, bool)))) | ((~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool)))),
% 1.33/1.15 inference(quant_inst,[status(thm)],[])).
% 1.33/1.15 tff(59,plain,
% 1.33/1.15 ((~![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, X), arr(ty_2Erealax_2Ereal, bool)))) | (~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))),
% 1.33/1.15 inference(modus_ponens,[status(thm)],[58, 57])).
% 1.33/1.15 tff(60,plain,
% 1.33/1.15 ((~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))),
% 1.33/1.15 inference(unit_resolution,[status(thm)],[59, 56])).
% 1.33/1.15 tff(61,plain,
% 1.33/1.15 (mem(ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))),
% 1.33/1.15 inference(unit_resolution,[status(thm)],[60, 49])).
% 1.33/1.15 tff(62,plain,
% 1.33/1.15 (mem(c_2Ereal__topology_2Eball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool))) <=> mem(c_2Ereal__topology_2Eball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))),
% 1.33/1.15 inference(rewrite,[status(thm)],[])).
% 1.33/1.15 tff(63,axiom,(mem(c_2Ereal__topology_2Eball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Ereal__topology_2Eball')).
% 1.33/1.15 tff(64,plain,
% 1.33/1.15 (mem(c_2Ereal__topology_2Eball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))),
% 1.33/1.15 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.33/1.15 tff(65,plain,
% 1.33/1.15 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ereal__topology_2Eball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))) | ![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, X), arr(ty_2Erealax_2Ereal, bool))))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ereal__topology_2Eball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))) | ![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, X), arr(ty_2Erealax_2Ereal, bool))))),
% 1.33/1.15 inference(rewrite,[status(thm)],[])).
% 1.33/1.15 tff(66,plain,
% 1.33/1.15 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ereal__topology_2Eball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))) | ![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, X), arr(ty_2Erealax_2Ereal, bool))))),
% 1.33/1.15 inference(quant_inst,[status(thm)],[])).
% 1.33/1.15 tff(67,plain,
% 1.33/1.15 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ereal__topology_2Eball, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), arr(ty_2Erealax_2Ereal, bool)))) | ![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, X), arr(ty_2Erealax_2Ereal, bool)))),
% 1.33/1.15 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.33/1.15 tff(68,plain,
% 1.33/1.15 (![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, X), arr(ty_2Erealax_2Ereal, bool)))),
% 1.33/1.15 inference(unit_resolution,[status(thm)],[67, 22, 64])).
% 1.33/1.15 tff(69,plain,
% 1.33/1.15 (((~![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, X), arr(ty_2Erealax_2Ereal, bool)))) | ((~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool)))) <=> ((~![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, X), arr(ty_2Erealax_2Ereal, bool)))) | (~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool)))),
% 1.33/1.15 inference(rewrite,[status(thm)],[])).
% 1.33/1.15 tff(70,plain,
% 1.33/1.15 ((~![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, X), arr(ty_2Erealax_2Ereal, bool)))) | ((~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool)))),
% 1.33/1.15 inference(quant_inst,[status(thm)],[])).
% 1.33/1.15 tff(71,plain,
% 1.33/1.15 ((~![X: $i] : ((~mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, X), arr(ty_2Erealax_2Ereal, bool)))) | (~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))),
% 1.33/1.15 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.33/1.15 tff(72,plain,
% 1.33/1.15 ((~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))),
% 1.33/1.15 inference(unit_resolution,[status(thm)],[71, 68])).
% 1.33/1.15 tff(73,plain,
% 1.33/1.15 (mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))),
% 1.33/1.15 inference(unit_resolution,[status(thm)],[72, 49])).
% 1.33/1.15 tff(74,plain,
% 1.33/1.15 (^[V0s: $i] : refl(((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))))) <=> ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))))))),
% 1.33/1.15 inference(bind,[status(th)],[])).
% 1.33/1.15 tff(75,plain,
% 1.33/1.15 (![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))))) <=> ![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))),
% 1.33/1.15 inference(quant_intro,[status(thm)],[74])).
% 1.33/1.15 tff(76,plain,
% 1.33/1.15 (^[V0s: $i] : rewrite(((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))))) <=> ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))))))),
% 1.33/1.15 inference(bind,[status(th)],[])).
% 1.33/1.15 tff(77,plain,
% 1.33/1.15 (![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))))) <=> ![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))),
% 1.33/1.15 inference(quant_intro,[status(thm)],[76])).
% 1.33/1.15 tff(78,plain,
% 1.33/1.15 (![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))))) <=> ![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))),
% 1.33/1.15 inference(transitivity,[status(thm)],[77, 75])).
% 1.33/1.15 tff(79,plain,
% 1.33/1.15 (^[V0s: $i] : rewrite(((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))))) <=> ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))))))),
% 1.33/1.15 inference(bind,[status(th)],[])).
% 1.33/1.15 tff(80,plain,
% 1.33/1.15 (![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))))) <=> ![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))),
% 1.33/1.15 inference(quant_intro,[status(thm)],[79])).
% 1.33/1.15 tff(81,plain,
% 1.33/1.15 (![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))))) <=> ![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool)))))),
% 1.33/1.15 inference(rewrite,[status(thm)],[])).
% 1.33/1.15 tff(82,plain,
% 1.33/1.15 (^[V0s: $i] : trans(monotonicity(quant_intro(proof_bind(^[V1t: $i] : trans(monotonicity(rewrite(((p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))) => p(ap(c_2Ereal__topology_2Ebounded__def, V0s))) <=> (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))), ((mem(V1t, arr(ty_2Erealax_2Ereal, bool)) => ((p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))) => p(ap(c_2Ereal__topology_2Ebounded__def, V0s)))) <=> (mem(V1t, arr(ty_2Erealax_2Ereal, bool)) => (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))))), rewrite((mem(V1t, arr(ty_2Erealax_2Ereal, bool)) => (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))) <=> (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))))), ((mem(V1t, arr(ty_2Erealax_2Ereal, bool)) => ((p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))) => p(ap(c_2Ereal__topology_2Ebounded__def, V0s)))) <=> (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))))))), (![V1t: $i] : (mem(V1t, arr(ty_2Erealax_2Ereal, bool)) => ((p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))) => p(ap(c_2Ereal__topology_2Ebounded__def, V0s)))) <=> ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool)))))), ((mem(V0s, arr(ty_2Erealax_2Ereal, bool)) => ![V1t: $i] : (mem(V1t, arr(ty_2Erealax_2Ereal, bool)) => ((p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))) => p(ap(c_2Ereal__topology_2Ebounded__def, V0s))))) <=> (mem(V0s, arr(ty_2Erealax_2Ereal, bool)) => ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))))))), rewrite((mem(V0s, arr(ty_2Erealax_2Ereal, bool)) => ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))))) <=> ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool)))))), ((mem(V0s, arr(ty_2Erealax_2Ereal, bool)) => ![V1t: $i] : (mem(V1t, arr(ty_2Erealax_2Ereal, bool)) => ((p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))) => p(ap(c_2Ereal__topology_2Ebounded__def, V0s))))) <=> ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool)))))))),
% 1.33/1.15 inference(bind,[status(th)],[])).
% 1.33/1.15 tff(83,plain,
% 1.33/1.15 (![V0s: $i] : (mem(V0s, arr(ty_2Erealax_2Ereal, bool)) => ![V1t: $i] : (mem(V1t, arr(ty_2Erealax_2Ereal, bool)) => ((p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))) => p(ap(c_2Ereal__topology_2Ebounded__def, V0s))))) <=> ![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool)))))),
% 1.33/1.15 inference(quant_intro,[status(thm)],[82])).
% 1.33/1.15 tff(84,axiom,(![V0s: $i] : (mem(V0s, arr(ty_2Erealax_2Ereal, bool)) => ![V1t: $i] : (mem(V1t, arr(ty_2Erealax_2Ereal, bool)) => ((p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t))) => p(ap(c_2Ereal__topology_2Ebounded__def, V0s)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Ereal__topology_2EBOUNDED__SUBSET')).
% 1.33/1.15 tff(85,plain,
% 1.33/1.15 (![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool)))))),
% 1.33/1.15 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.33/1.15 tff(86,plain,
% 1.33/1.15 (![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool)))))),
% 1.33/1.15 inference(modus_ponens,[status(thm)],[85, 81])).
% 1.33/1.15 tff(87,plain,(
% 1.33/1.15 ![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~(p(ap(c_2Ereal__topology_2Ebounded__def, V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool)))))),
% 1.33/1.15 inference(skolemize,[status(sab)],[86])).
% 1.33/1.15 tff(88,plain,
% 1.33/1.15 (![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))),
% 1.33/1.15 inference(modus_ponens,[status(thm)],[87, 80])).
% 1.33/1.15 tff(89,plain,
% 1.33/1.15 (![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))),
% 1.33/1.15 inference(modus_ponens,[status(thm)],[88, 78])).
% 1.33/1.15 tff(90,plain,
% 1.33/1.15 (((~![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))) | ((~mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : ((~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t)))))) <=> ((~![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))) | (~mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : ((~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t)))))),
% 1.33/1.15 inference(rewrite,[status(thm)],[])).
% 1.33/1.15 tff(91,plain,
% 1.33/1.15 (((~mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t))))) <=> ((~mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : ((~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t)))))),
% 1.33/1.15 inference(rewrite,[status(thm)],[])).
% 1.33/1.15 tff(92,plain,
% 1.33/1.15 (((~![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))) | ((~mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t)))))) <=> ((~![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))) | ((~mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : ((~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t))))))),
% 1.33/1.15 inference(monotonicity,[status(thm)],[91])).
% 1.33/1.15 tff(93,plain,
% 1.33/1.15 (((~![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))) | ((~mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t)))))) <=> ((~![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))) | (~mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : ((~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t)))))),
% 1.33/1.15 inference(transitivity,[status(thm)],[92, 90])).
% 1.33/1.15 tff(94,plain,
% 1.33/1.15 ((~![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))) | ((~mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t)))))),
% 1.33/1.15 inference(quant_inst,[status(thm)],[])).
% 1.33/1.15 tff(95,plain,
% 1.33/1.15 ((~![V0s: $i] : ((~mem(V0s, arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : (p(ap(c_2Ereal__topology_2Ebounded__def, V0s)) | (~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), V0s), V1t)))))) | (~mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : ((~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t))))),
% 1.33/1.15 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.33/1.15 tff(96,plain,
% 1.33/1.15 ((~mem(ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | ![V1t: $i] : ((~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t))))),
% 1.33/1.15 inference(unit_resolution,[status(thm)],[95, 89])).
% 1.33/1.15 tff(97,plain,
% 1.33/1.15 (![V1t: $i] : ((~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t))))),
% 1.33/1.15 inference(unit_resolution,[status(thm)],[96, 73])).
% 1.33/1.15 tff(98,plain,
% 1.33/1.15 (^[V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : refl(p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e))))) <=> p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e))))))),
% 1.33/1.15 inference(bind,[status(th)],[])).
% 1.33/1.15 tff(99,plain,
% 1.33/1.15 (![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e))))) <=> ![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.33/1.16 inference(quant_intro,[status(thm)],[98])).
% 1.33/1.16 tff(100,plain,
% 1.33/1.16 (![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e))))) <=> ![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.33/1.16 inference(rewrite,[status(thm)],[])).
% 1.33/1.16 tff(101,axiom,(![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Ereal__topology_2EBOUNDED__CBALL')).
% 1.33/1.16 tff(102,plain,
% 1.33/1.16 (![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.33/1.16 inference(modus_ponens,[status(thm)],[101, 100])).
% 1.33/1.16 tff(103,plain,(
% 1.33/1.16 ![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.33/1.16 inference(skolemize,[status(sab)],[102])).
% 1.33/1.16 tff(104,plain,
% 1.33/1.16 (![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.33/1.16 inference(modus_ponens,[status(thm)],[103, 99])).
% 1.33/1.16 tff(105,plain,
% 1.33/1.16 ((~![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))))),
% 1.33/1.16 inference(quant_inst,[status(thm)],[])).
% 1.33/1.16 tff(106,plain,
% 1.33/1.16 (p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))))),
% 1.33/1.16 inference(unit_resolution,[status(thm)],[105, 104])).
% 1.33/1.16 tff(107,plain,
% 1.33/1.16 (^[V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : refl(p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e))))) <=> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e))))))),
% 1.45/1.16 inference(bind,[status(th)],[])).
% 1.45/1.16 tff(108,plain,
% 1.45/1.16 (![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e))))) <=> ![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.45/1.16 inference(quant_intro,[status(thm)],[107])).
% 1.45/1.16 tff(109,plain,
% 1.45/1.16 (![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e))))) <=> ![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.45/1.16 inference(rewrite,[status(thm)],[])).
% 1.45/1.16 tff(110,axiom,(![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Ereal__topology_2EBALL__SUBSET__CBALL')).
% 1.45/1.16 tff(111,plain,
% 1.45/1.16 (![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.45/1.16 tff(112,plain,(
% 1.45/1.16 ![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.45/1.16 inference(skolemize,[status(sab)],[111])).
% 1.45/1.16 tff(113,plain,
% 1.45/1.16 (![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[112, 108])).
% 1.45/1.16 tff(114,plain,
% 1.45/1.16 ((~![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))) | p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))))),
% 1.45/1.16 inference(quant_inst,[status(thm)],[])).
% 1.45/1.16 tff(115,plain,
% 1.45/1.16 (p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))))),
% 1.45/1.16 inference(unit_resolution,[status(thm)],[114, 113])).
% 1.45/1.16 tff(116,plain,
% 1.45/1.16 ((~![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))) <=> (~![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e))))))),
% 1.45/1.16 inference(rewrite,[status(thm)],[])).
% 1.45/1.16 tff(117,axiom,(~![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Ereal__topology_2EBOUNDED__BALL')).
% 1.45/1.16 tff(118,plain,
% 1.45/1.16 (~![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.45/1.16 tff(119,plain,
% 1.45/1.16 (~![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[118, 116])).
% 1.45/1.16 tff(120,plain,
% 1.45/1.16 (~![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[119, 116])).
% 1.45/1.16 tff(121,plain,
% 1.45/1.16 (~![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[120, 116])).
% 1.45/1.16 tff(122,plain,
% 1.45/1.16 (~![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[121, 116])).
% 1.45/1.16 tff(123,plain,
% 1.45/1.16 (~![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[122, 116])).
% 1.45/1.16 tff(124,plain,
% 1.45/1.16 (~![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[123, 116])).
% 1.45/1.16 tff(125,plain,
% 1.45/1.16 (~![V0x: tp__ty_2Erealax_2Ereal, V1e: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x)), inj__ty_2Erealax_2Ereal(V1e)))))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[124, 116])).
% 1.45/1.16 tff(126,plain,(
% 1.45/1.16 ~p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))))),
% 1.45/1.16 inference(skolemize,[status(sab)],[125])).
% 1.45/1.16 tff(127,plain,
% 1.45/1.16 (((~![V1t: $i] : ((~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t))))) | ((~mem(ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))))))) <=> ((~![V1t: $i] : ((~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t))))) | (~mem(ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))))))),
% 1.45/1.16 inference(rewrite,[status(thm)],[])).
% 1.45/1.16 tff(128,plain,
% 1.45/1.16 ((~![V1t: $i] : ((~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t))))) | ((~mem(ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))))))),
% 1.45/1.16 inference(quant_inst,[status(thm)],[])).
% 1.45/1.16 tff(129,plain,
% 1.45/1.16 ((~![V1t: $i] : ((~mem(V1t, arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, V1t))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), V1t))))) | (~mem(ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))), arr(ty_2Erealax_2Ereal, bool))) | p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))) | (~p(ap(c_2Ereal__topology_2Ebounded__def, ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))))) | (~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal), ap(c_2Ereal__topology_2Eball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5)))), ap(c_2Ereal__topology_2Ecball, ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), inj__ty_2Erealax_2Ereal(V0x!6)), inj__ty_2Erealax_2Ereal(V1e!5))))))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.45/1.16 tff(130,plain,
% 1.45/1.16 ($false),
% 1.45/1.16 inference(unit_resolution,[status(thm)],[129, 126, 115, 106, 97, 61])).
% 1.45/1.16 % SZS output end Proof
%------------------------------------------------------------------------------