TSTP Solution File: ITP018_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP018_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 04:15:17 EDT 2022
% Result : Theorem 0.13s 0.32s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : ITP018_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.04/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.28 % Computer : n020.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Thu Sep 1 03:12:15 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.29 Usage: tptp [options] [-file:]file
% 0.09/0.29 -h, -? prints this message.
% 0.09/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.29 -m, -model generate model.
% 0.09/0.29 -p, -proof generate proof.
% 0.09/0.29 -c, -core generate unsat core of named formulas.
% 0.09/0.29 -st, -statistics display statistics.
% 0.09/0.29 -t:timeout set timeout (in second).
% 0.09/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.29 -<param>:<value> configuration parameter and value.
% 0.09/0.29 -o:<output-file> file to place output in.
% 0.13/0.32 % SZS status Theorem
% 0.13/0.32 % SZS output start Proof
% 0.13/0.32 tff(surj__ty_2Erealax_2Ereal_type, type, (
% 0.13/0.32 surj__ty_2Erealax_2Ereal: $i > tp__ty_2Erealax_2Ereal)).
% 0.13/0.32 tff(ap_type, type, (
% 0.13/0.32 ap: ( $i * $i ) > $i)).
% 0.13/0.32 tff(c_2Ebool_2Ethe__value_type, type, (
% 0.13/0.32 c_2Ebool_2Ethe__value: del > $i)).
% 0.13/0.32 tff(ty_2Epair_2Eprod_type, type, (
% 0.13/0.32 ty_2Epair_2Eprod: ( del * del ) > del)).
% 0.13/0.32 tff(tptp_fun_A_27w_2_type, type, (
% 0.13/0.32 tptp_fun_A_27w_2: del)).
% 0.13/0.32 tff(tptp_fun_A_27t_3_type, type, (
% 0.13/0.32 tptp_fun_A_27t_3: del)).
% 0.13/0.32 tff(c_2Ebinary__ieee_2Efloat__plus__min_type, type, (
% 0.13/0.32 c_2Ebinary__ieee_2Efloat__plus__min: ( del * del ) > $i)).
% 0.13/0.32 tff(c_2Ebinary__ieee_2Efloat__negate_type, type, (
% 0.13/0.32 c_2Ebinary__ieee_2Efloat__negate: ( del * del ) > $i)).
% 0.13/0.32 tff(c_2Ebinary__ieee_2Efloat__to__real_type, type, (
% 0.13/0.32 c_2Ebinary__ieee_2Efloat__to__real: ( del * del ) > $i)).
% 0.13/0.32 tff(c_2Ebinary__ieee_2Eulp_type, type, (
% 0.13/0.32 c_2Ebinary__ieee_2Eulp: ( del * del ) > $i)).
% 0.13/0.32 tff(c_2Erealax_2Ereal__neg_type, type, (
% 0.13/0.32 c_2Erealax_2Ereal__neg: $i)).
% 0.13/0.32 tff(mem_type, type, (
% 0.13/0.32 mem: ( $i * del ) > $o)).
% 0.13/0.32 tff(ty_2Ebinary__ieee_2Efloat_type, type, (
% 0.13/0.32 ty_2Ebinary__ieee_2Efloat: ( del * del ) > del)).
% 0.13/0.32 tff(ty_2Ebool_2Eitself_type, type, (
% 0.13/0.32 ty_2Ebool_2Eitself: del > del)).
% 0.13/0.32 tff(arr_type, type, (
% 0.13/0.32 arr: ( del * del ) > del)).
% 0.13/0.32 tff(inj__ty_2Erealax_2Ereal_type, type, (
% 0.13/0.32 inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i)).
% 0.13/0.32 tff(ty_2Erealax_2Ereal_type, type, (
% 0.13/0.32 ty_2Erealax_2Ereal: del)).
% 0.13/0.32 tff(1,plain,
% 0.13/0.32 (^[A_27t: del, A_27w: del] : refl(mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Ebinary__ieee_2Efloat(A_27t, A_27w))) <=> mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Ebinary__ieee_2Efloat(A_27t, A_27w))))),
% 0.13/0.32 inference(bind,[status(th)],[])).
% 0.13/0.32 tff(2,plain,
% 0.13/0.32 (![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Ebinary__ieee_2Efloat(A_27t, A_27w))) <=> ![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Ebinary__ieee_2Efloat(A_27t, A_27w)))),
% 0.13/0.32 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.32 tff(3,plain,
% 0.13/0.32 (![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Ebinary__ieee_2Efloat(A_27t, A_27w))) <=> ![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Ebinary__ieee_2Efloat(A_27t, A_27w)))),
% 0.13/0.32 inference(rewrite,[status(thm)],[])).
% 0.13/0.32 tff(4,axiom,(![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Ebinary__ieee_2Efloat(A_27t, A_27w)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Ebinary__ieee_2Efloat__plus__min')).
% 0.13/0.32 tff(5,plain,
% 0.13/0.32 (![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Ebinary__ieee_2Efloat(A_27t, A_27w)))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.32 tff(6,plain,(
% 0.13/0.32 ![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Ebinary__ieee_2Efloat(A_27t, A_27w)))),
% 0.13/0.32 inference(skolemize,[status(sab)],[5])).
% 0.13/0.32 tff(7,plain,
% 0.13/0.32 (![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Ebinary__ieee_2Efloat(A_27t, A_27w)))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.32 tff(8,plain,
% 0.13/0.32 ((~![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Ebinary__ieee_2Efloat(A_27t, A_27w)))) | mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))),
% 0.13/0.32 inference(quant_inst,[status(thm)],[])).
% 0.13/0.32 tff(9,plain,
% 0.13/0.32 (mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))),
% 0.13/0.32 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.32 tff(10,plain,
% 0.13/0.32 (^[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))))),
% 0.13/0.32 inference(bind,[status(th)],[])).
% 0.13/0.32 tff(11,plain,
% 0.13/0.32 (![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)))),
% 0.13/0.32 inference(quant_intro,[status(thm)],[10])).
% 0.13/0.32 tff(12,plain,
% 0.13/0.32 (^[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))))),
% 0.13/0.32 inference(bind,[status(th)],[])).
% 0.13/0.32 tff(13,plain,
% 0.13/0.32 (![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)))),
% 0.13/0.32 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.32 tff(14,plain,
% 0.13/0.32 (![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)))),
% 0.13/0.32 inference(transitivity,[status(thm)],[13, 11])).
% 0.13/0.32 tff(15,plain,
% 0.13/0.32 (![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)))),
% 0.13/0.32 inference(rewrite,[status(thm)],[])).
% 0.13/0.32 tff(16,plain,
% 0.13/0.32 (^[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)))))),
% 0.13/0.32 inference(bind,[status(th)],[])).
% 0.13/0.32 tff(17,plain,
% 0.13/0.32 (![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)))),
% 0.13/0.32 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.32 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')).
% 0.13/0.32 tff(19,plain,
% 0.13/0.32 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.32 tff(20,plain,
% 0.13/0.32 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.13/0.32 tff(21,plain,(
% 0.13/0.32 ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 0.13/0.32 inference(skolemize,[status(sab)],[20])).
% 0.13/0.32 tff(22,plain,
% 0.13/0.32 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.13/0.32 tff(23,plain,
% 0.13/0.32 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))) | ![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), X), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))) | ![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), X), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))))),
% 0.13/0.32 inference(rewrite,[status(thm)],[])).
% 0.13/0.32 tff(24,plain,
% 0.13/0.32 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))) | ![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), X), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))))),
% 0.13/0.32 inference(quant_inst,[status(thm)],[])).
% 0.13/0.32 tff(25,plain,
% 0.13/0.32 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))) | ![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), X), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.32 tff(26,plain,
% 0.13/0.32 (![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), X), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))),
% 0.13/0.32 inference(unit_resolution,[status(thm)],[25, 22, 9])).
% 0.13/0.32 tff(27,plain,
% 0.13/0.32 (^[A_27a: del] : refl(mem(c_2Ebool_2Ethe__value(A_27a), ty_2Ebool_2Eitself(A_27a)) <=> mem(c_2Ebool_2Ethe__value(A_27a), ty_2Ebool_2Eitself(A_27a)))),
% 0.13/0.32 inference(bind,[status(th)],[])).
% 0.13/0.32 tff(28,plain,
% 0.13/0.32 (![A_27a: del] : mem(c_2Ebool_2Ethe__value(A_27a), ty_2Ebool_2Eitself(A_27a)) <=> ![A_27a: del] : mem(c_2Ebool_2Ethe__value(A_27a), ty_2Ebool_2Eitself(A_27a))),
% 0.13/0.32 inference(quant_intro,[status(thm)],[27])).
% 0.13/0.32 tff(29,plain,
% 0.13/0.32 (![A_27a: del] : mem(c_2Ebool_2Ethe__value(A_27a), ty_2Ebool_2Eitself(A_27a)) <=> ![A_27a: del] : mem(c_2Ebool_2Ethe__value(A_27a), ty_2Ebool_2Eitself(A_27a))),
% 0.13/0.32 inference(rewrite,[status(thm)],[])).
% 0.13/0.32 tff(30,axiom,(![A_27a: del] : mem(c_2Ebool_2Ethe__value(A_27a), ty_2Ebool_2Eitself(A_27a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Ebool_2Ethe__value')).
% 0.13/0.32 tff(31,plain,
% 0.13/0.32 (![A_27a: del] : mem(c_2Ebool_2Ethe__value(A_27a), ty_2Ebool_2Eitself(A_27a))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.32 tff(32,plain,(
% 0.13/0.32 ![A_27a: del] : mem(c_2Ebool_2Ethe__value(A_27a), ty_2Ebool_2Eitself(A_27a))),
% 0.13/0.32 inference(skolemize,[status(sab)],[31])).
% 0.13/0.32 tff(33,plain,
% 0.13/0.32 (![A_27a: del] : mem(c_2Ebool_2Ethe__value(A_27a), ty_2Ebool_2Eitself(A_27a))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.13/0.32 tff(34,plain,
% 0.13/0.32 ((~![A_27a: del] : mem(c_2Ebool_2Ethe__value(A_27a), ty_2Ebool_2Eitself(A_27a))) | mem(c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))),
% 0.13/0.32 inference(quant_inst,[status(thm)],[])).
% 0.13/0.32 tff(35,plain,
% 0.13/0.32 (mem(c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))),
% 0.13/0.32 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.13/0.32 tff(36,plain,
% 0.13/0.32 (((~![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), X), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))) | ((~mem(c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))) <=> ((~![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), X), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))) | (~mem(c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))),
% 0.13/0.32 inference(rewrite,[status(thm)],[])).
% 0.13/0.32 tff(37,plain,
% 0.13/0.32 ((~![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), X), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))) | ((~mem(c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))),
% 0.13/0.32 inference(quant_inst,[status(thm)],[])).
% 0.13/0.32 tff(38,plain,
% 0.13/0.32 ((~![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), X), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2)))) | (~mem(c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.32 tff(39,plain,
% 0.13/0.32 (mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))),
% 0.13/0.32 inference(unit_resolution,[status(thm)],[38, 35, 26])).
% 0.13/0.32 tff(40,plain,
% 0.13/0.32 (^[A_27a: del, A_27b: del, V0x: $i] : refl(((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x))))) <=> ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x))))))),
% 0.13/0.32 inference(bind,[status(th)],[])).
% 0.13/0.32 tff(41,plain,
% 0.13/0.32 (![A_27a: del, A_27b: del, V0x: $i] : ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x))))) <=> ![A_27a: del, A_27b: del, V0x: $i] : ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x)))))),
% 0.13/0.32 inference(quant_intro,[status(thm)],[40])).
% 0.13/0.32 tff(42,plain,
% 0.13/0.32 (![A_27a: del, A_27b: del, V0x: $i] : ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x))))) <=> ![A_27a: del, A_27b: del, V0x: $i] : ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x)))))),
% 0.13/0.32 inference(rewrite,[status(thm)],[])).
% 0.13/0.32 tff(43,plain,
% 0.13/0.32 (^[A_27a: del, A_27b: del, V0x: $i] : rewrite((mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b)) => (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x))))) <=> ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x))))))),
% 0.13/0.32 inference(bind,[status(th)],[])).
% 0.13/0.32 tff(44,plain,
% 0.13/0.32 (![A_27a: del, A_27b: del, V0x: $i] : (mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b)) => (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x))))) <=> ![A_27a: del, A_27b: del, V0x: $i] : ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x)))))),
% 0.13/0.32 inference(quant_intro,[status(thm)],[43])).
% 0.13/0.32 tff(45,axiom,(![A_27a: del, A_27b: del, V0x: $i] : (mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b)) => (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Ebinary__ieee_2Efloat__to__real__negate')).
% 0.13/0.32 tff(46,plain,
% 0.13/0.32 (![A_27a: del, A_27b: del, V0x: $i] : ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x)))))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.13/0.32 tff(47,plain,
% 0.13/0.32 (![A_27a: del, A_27b: del, V0x: $i] : ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x)))))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.13/0.32 tff(48,plain,(
% 0.13/0.32 ![A_27a: del, A_27b: del, V0x: $i] : ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x)))))),
% 0.13/0.32 inference(skolemize,[status(sab)],[47])).
% 0.13/0.32 tff(49,plain,
% 0.13/0.32 (![A_27a: del, A_27b: del, V0x: $i] : ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x)))))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.13/0.32 tff(50,plain,
% 0.13/0.32 (((~![A_27a: del, A_27b: del, V0x: $i] : ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x)))))) | ((~mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))))) <=> ((~![A_27a: del, A_27b: del, V0x: $i] : ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x)))))) | (~mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))))),
% 0.13/0.32 inference(rewrite,[status(thm)],[])).
% 0.13/0.32 tff(51,plain,
% 0.13/0.32 ((~![A_27a: del, A_27b: del, V0x: $i] : ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x)))))) | ((~mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))))),
% 0.13/0.32 inference(quant_inst,[status(thm)],[])).
% 0.13/0.32 tff(52,plain,
% 0.13/0.32 ((~![A_27a: del, A_27b: del, V0x: $i] : ((~mem(V0x, ty_2Ebinary__ieee_2Efloat(A_27a, A_27b))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), ap(c_2Ebinary__ieee_2Efloat__negate(A_27a, A_27b), V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a, A_27b), V0x)))))) | (~mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.13/0.32 tff(53,plain,
% 0.13/0.32 ((~mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))))),
% 0.13/0.32 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.13/0.32 tff(54,plain,
% 0.13/0.32 (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))),
% 0.13/0.32 inference(unit_resolution,[status(thm)],[53, 39])).
% 0.13/0.32 tff(55,plain,
% 0.13/0.32 (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))),
% 0.13/0.32 inference(symmetry,[status(thm)],[54])).
% 0.13/0.32 tff(56,plain,
% 0.13/0.32 (^[A_27t: del, A_27w: del] : refl(mem(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Erealax_2Ereal)) <=> mem(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Erealax_2Ereal)))),
% 0.13/0.32 inference(bind,[status(th)],[])).
% 0.13/0.32 tff(57,plain,
% 0.13/0.32 (![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Erealax_2Ereal)) <=> ![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Erealax_2Ereal))),
% 0.13/0.32 inference(quant_intro,[status(thm)],[56])).
% 0.13/0.32 tff(58,plain,
% 0.13/0.32 (![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Erealax_2Ereal)) <=> ![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Erealax_2Ereal))),
% 0.13/0.32 inference(rewrite,[status(thm)],[])).
% 0.13/0.32 tff(59,axiom,(![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Erealax_2Ereal))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Ebinary__ieee_2Eulp')).
% 0.13/0.32 tff(60,plain,
% 0.13/0.32 (![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Erealax_2Ereal))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.13/0.32 tff(61,plain,(
% 0.13/0.32 ![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Erealax_2Ereal))),
% 0.13/0.32 inference(skolemize,[status(sab)],[60])).
% 0.13/0.32 tff(62,plain,
% 0.13/0.32 (![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Erealax_2Ereal))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.13/0.32 tff(63,plain,
% 0.13/0.32 ((~![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t, A_27w)), ty_2Erealax_2Ereal))) | mem(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Erealax_2Ereal))),
% 0.13/0.32 inference(quant_inst,[status(thm)],[])).
% 0.13/0.32 tff(64,plain,
% 0.13/0.32 (mem(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Erealax_2Ereal))),
% 0.13/0.32 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.13/0.32 tff(65,plain,
% 0.13/0.32 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Erealax_2Ereal))) | ![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), X), 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_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Erealax_2Ereal))) | ![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal)))),
% 0.13/0.32 inference(rewrite,[status(thm)],[])).
% 0.13/0.32 tff(66,plain,
% 0.13/0.32 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Erealax_2Ereal))) | ![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal)))),
% 0.13/0.32 inference(quant_inst,[status(thm)],[])).
% 0.13/0.32 tff(67,plain,
% 0.13/0.32 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Erealax_2Ereal))) | ![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal))),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.13/0.32 tff(68,plain,
% 0.13/0.32 (![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal))),
% 0.13/0.32 inference(unit_resolution,[status(thm)],[67, 22, 64])).
% 0.13/0.32 tff(69,plain,
% 0.13/0.32 (((~![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal))) | ((~mem(c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Erealax_2Ereal))) <=> ((~![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal))) | (~mem(c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Erealax_2Ereal))),
% 0.13/0.32 inference(rewrite,[status(thm)],[])).
% 0.13/0.32 tff(70,plain,
% 0.13/0.32 ((~![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal))) | ((~mem(c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Erealax_2Ereal))),
% 0.13/0.32 inference(quant_inst,[status(thm)],[])).
% 0.13/0.32 tff(71,plain,
% 0.13/0.32 ((~![X: $i] : ((~mem(X, ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal))) | (~mem(c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)), ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) | mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Erealax_2Ereal)),
% 0.13/0.32 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.13/0.32 tff(72,plain,
% 0.13/0.32 (mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Erealax_2Ereal)),
% 0.13/0.32 inference(unit_resolution,[status(thm)],[71, 35, 68])).
% 0.13/0.32 tff(73,plain,
% 0.13/0.32 (^[X: $i] : refl(((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X)))) <=> ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X)))))),
% 0.13/0.32 inference(bind,[status(th)],[])).
% 0.13/0.32 tff(74,plain,
% 0.13/0.32 (![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X)))) <=> ![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))),
% 0.13/0.32 inference(quant_intro,[status(thm)],[73])).
% 0.13/0.32 tff(75,plain,
% 0.13/0.32 (![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X)))) <=> ![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))),
% 0.13/0.32 inference(rewrite,[status(thm)],[])).
% 0.13/0.32 tff(76,plain,
% 0.13/0.32 (^[X: $i] : rewrite((mem(X, ty_2Erealax_2Ereal) => (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X)))) <=> ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X)))))),
% 0.13/0.33 inference(bind,[status(th)],[])).
% 0.13/0.33 tff(77,plain,
% 0.13/0.33 (![X: $i] : (mem(X, ty_2Erealax_2Ereal) => (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X)))) <=> ![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))),
% 0.13/0.33 inference(quant_intro,[status(thm)],[76])).
% 0.13/0.33 tff(78,axiom,(![X: $i] : (mem(X, ty_2Erealax_2Ereal) => (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','stp_iso_mem_ty_2Erealax_2Ereal')).
% 0.13/0.33 tff(79,plain,
% 0.13/0.33 (![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.13/0.33 tff(80,plain,
% 0.13/0.33 (![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.13/0.33 tff(81,plain,(
% 0.13/0.33 ![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))),
% 0.13/0.33 inference(skolemize,[status(sab)],[80])).
% 0.13/0.33 tff(82,plain,
% 0.13/0.33 (![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.13/0.33 tff(83,plain,
% 0.13/0.33 (((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))) | ((~mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Erealax_2Ereal)) | (ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))))) <=> ((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))) | (~mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Erealax_2Ereal)) | (ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))))),
% 0.13/0.33 inference(rewrite,[status(thm)],[])).
% 0.13/0.33 tff(84,plain,
% 0.13/0.33 ((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))) | ((~mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Erealax_2Ereal)) | (ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))))),
% 0.13/0.33 inference(quant_inst,[status(thm)],[])).
% 0.13/0.33 tff(85,plain,
% 0.13/0.33 ((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))) | (~mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Erealax_2Ereal)) | (ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.13/0.33 tff(86,plain,
% 0.13/0.33 ((~mem(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Erealax_2Ereal)) | (ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))),
% 0.13/0.33 inference(unit_resolution,[status(thm)],[85, 82])).
% 0.13/0.33 tff(87,plain,
% 0.13/0.33 (ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))),
% 0.13/0.33 inference(unit_resolution,[status(thm)],[86, 72])).
% 0.13/0.33 tff(88,plain,
% 0.13/0.33 (inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))) = ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))),
% 0.13/0.33 inference(symmetry,[status(thm)],[87])).
% 0.13/0.33 tff(89,plain,
% 0.13/0.33 (^[A_27t: del, A_27w: del] : refl((surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))) <=> (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))))),
% 0.13/0.33 inference(bind,[status(th)],[])).
% 0.13/0.33 tff(90,plain,
% 0.13/0.33 (![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))) <=> ![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))))),
% 0.13/0.33 inference(quant_intro,[status(thm)],[89])).
% 0.13/0.33 tff(91,plain,
% 0.13/0.33 (![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))) <=> ![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))))),
% 0.13/0.33 inference(rewrite,[status(thm)],[])).
% 0.13/0.33 tff(92,axiom,(![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Ebinary__ieee_2Eulp')).
% 0.13/0.33 tff(93,plain,
% 0.13/0.33 (![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.13/0.33 tff(94,plain,(
% 0.13/0.33 ![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))))),
% 0.13/0.33 inference(skolemize,[status(sab)],[93])).
% 0.13/0.33 tff(95,plain,
% 0.13/0.33 (![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.13/0.33 tff(96,plain,
% 0.13/0.33 ((~![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))))) | (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))),
% 0.13/0.33 inference(quant_inst,[status(thm)],[])).
% 0.13/0.33 tff(97,plain,
% 0.13/0.33 (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))),
% 0.13/0.33 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.13/0.33 tff(98,plain,
% 0.13/0.33 (inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))),
% 0.13/0.33 inference(monotonicity,[status(thm)],[97])).
% 0.13/0.33 tff(99,plain,
% 0.13/0.33 (inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))),
% 0.13/0.33 inference(symmetry,[status(thm)],[98])).
% 0.13/0.33 tff(100,plain,
% 0.13/0.33 (^[A_27t: del, A_27w: del] : refl(mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), arr(ty_2Ebinary__ieee_2Efloat(A_27t, A_27w), ty_2Erealax_2Ereal)) <=> mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), arr(ty_2Ebinary__ieee_2Efloat(A_27t, A_27w), ty_2Erealax_2Ereal)))),
% 0.13/0.33 inference(bind,[status(th)],[])).
% 0.13/0.33 tff(101,plain,
% 0.13/0.33 (![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), arr(ty_2Ebinary__ieee_2Efloat(A_27t, A_27w), ty_2Erealax_2Ereal)) <=> ![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), arr(ty_2Ebinary__ieee_2Efloat(A_27t, A_27w), ty_2Erealax_2Ereal))),
% 0.13/0.33 inference(quant_intro,[status(thm)],[100])).
% 0.13/0.33 tff(102,plain,
% 0.13/0.33 (![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), arr(ty_2Ebinary__ieee_2Efloat(A_27t, A_27w), ty_2Erealax_2Ereal)) <=> ![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), arr(ty_2Ebinary__ieee_2Efloat(A_27t, A_27w), ty_2Erealax_2Ereal))),
% 0.13/0.33 inference(rewrite,[status(thm)],[])).
% 0.13/0.33 tff(103,axiom,(![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), arr(ty_2Ebinary__ieee_2Efloat(A_27t, A_27w), ty_2Erealax_2Ereal))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Ebinary__ieee_2Efloat__to__real')).
% 0.13/0.33 tff(104,plain,
% 0.13/0.33 (![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), arr(ty_2Ebinary__ieee_2Efloat(A_27t, A_27w), ty_2Erealax_2Ereal))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.13/0.33 tff(105,plain,(
% 0.13/0.33 ![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), arr(ty_2Ebinary__ieee_2Efloat(A_27t, A_27w), ty_2Erealax_2Ereal))),
% 0.13/0.33 inference(skolemize,[status(sab)],[104])).
% 0.13/0.33 tff(106,plain,
% 0.13/0.33 (![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), arr(ty_2Ebinary__ieee_2Efloat(A_27t, A_27w), ty_2Erealax_2Ereal))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.13/0.33 tff(107,plain,
% 0.13/0.33 ((~![A_27t: del, A_27w: del] : mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), arr(ty_2Ebinary__ieee_2Efloat(A_27t, A_27w), ty_2Erealax_2Ereal))) | mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), arr(ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2), ty_2Erealax_2Ereal))),
% 0.13/0.33 inference(quant_inst,[status(thm)],[])).
% 0.13/0.33 tff(108,plain,
% 0.13/0.33 (mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), arr(ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2), ty_2Erealax_2Ereal))),
% 0.13/0.33 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.13/0.33 tff(109,plain,
% 0.13/0.33 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), arr(ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2), ty_2Erealax_2Ereal))) | ![X: $i] : ((~mem(X, ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), X), 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_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), arr(ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2), ty_2Erealax_2Ereal))) | ![X: $i] : ((~mem(X, ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal)))),
% 0.13/0.33 inference(rewrite,[status(thm)],[])).
% 0.13/0.33 tff(110,plain,
% 0.13/0.33 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), arr(ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2), ty_2Erealax_2Ereal))) | ![X: $i] : ((~mem(X, ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal)))),
% 0.13/0.33 inference(quant_inst,[status(thm)],[])).
% 0.13/0.33 tff(111,plain,
% 0.13/0.33 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), arr(ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2), ty_2Erealax_2Ereal))) | ![X: $i] : ((~mem(X, ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.13/0.33 tff(112,plain,
% 0.13/0.33 (![X: $i] : ((~mem(X, ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal))),
% 0.13/0.33 inference(unit_resolution,[status(thm)],[111, 22, 108])).
% 0.13/0.33 tff(113,plain,
% 0.13/0.33 (((~![X: $i] : ((~mem(X, ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal))) | ((~mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))), ty_2Erealax_2Ereal))) <=> ((~![X: $i] : ((~mem(X, ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal))) | (~mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))), ty_2Erealax_2Ereal))),
% 0.13/0.33 inference(rewrite,[status(thm)],[])).
% 0.13/0.33 tff(114,plain,
% 0.13/0.33 ((~![X: $i] : ((~mem(X, ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal))) | ((~mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))), ty_2Erealax_2Ereal))),
% 0.13/0.33 inference(quant_inst,[status(thm)],[])).
% 0.13/0.33 tff(115,plain,
% 0.13/0.33 ((~![X: $i] : ((~mem(X, ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), X), ty_2Erealax_2Ereal))) | (~mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))), ty_2Ebinary__ieee_2Efloat(A_27t!3, A_27w!2))) | mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))), ty_2Erealax_2Ereal)),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.13/0.33 tff(116,plain,
% 0.13/0.33 (mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))), ty_2Erealax_2Ereal)),
% 0.13/0.33 inference(unit_resolution,[status(thm)],[115, 39, 112])).
% 0.13/0.33 tff(117,plain,
% 0.13/0.33 (((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))) | ((~mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))), ty_2Erealax_2Ereal)) | (ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))))) <=> ((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))) | (~mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))), ty_2Erealax_2Ereal)) | (ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))))),
% 0.13/0.33 inference(rewrite,[status(thm)],[])).
% 0.13/0.33 tff(118,plain,
% 0.13/0.33 ((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))) | ((~mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))), ty_2Erealax_2Ereal)) | (ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))))),
% 0.13/0.33 inference(quant_inst,[status(thm)],[])).
% 0.13/0.33 tff(119,plain,
% 0.13/0.33 ((~![X: $i] : ((~mem(X, ty_2Erealax_2Ereal)) | (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X))))) | (~mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))), ty_2Erealax_2Ereal)) | (ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.13/0.33 tff(120,plain,
% 0.13/0.33 ((~mem(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))), ty_2Erealax_2Ereal)) | (ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))))),
% 0.13/0.33 inference(unit_resolution,[status(thm)],[119, 82])).
% 0.13/0.33 tff(121,plain,
% 0.13/0.33 (ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))),
% 0.13/0.33 inference(unit_resolution,[status(thm)],[120, 116])).
% 0.13/0.33 tff(122,plain,
% 0.13/0.33 (ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) = ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))),
% 0.13/0.33 inference(transitivity,[status(thm)],[121, 99, 88])).
% 0.13/0.33 tff(123,plain,
% 0.13/0.33 (ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))) = ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))),
% 0.13/0.33 inference(monotonicity,[status(thm)],[122])).
% 0.13/0.33 tff(124,plain,
% 0.13/0.33 (ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))) = ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))),
% 0.13/0.33 inference(symmetry,[status(thm)],[123])).
% 0.13/0.33 tff(125,plain,
% 0.13/0.33 (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))),
% 0.13/0.33 inference(monotonicity,[status(thm)],[124])).
% 0.13/0.33 tff(126,plain,
% 0.13/0.33 (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))))),
% 0.13/0.33 inference(transitivity,[status(thm)],[125, 55])).
% 0.13/0.33 tff(127,plain,
% 0.13/0.33 ((~![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))))) <=> (~![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))))))),
% 0.13/0.33 inference(rewrite,[status(thm)],[])).
% 0.13/0.33 tff(128,axiom,(~![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Ebinary__ieee_2Eneg__ulp')).
% 0.13/0.33 tff(129,plain,
% 0.13/0.33 (~![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.13/0.33 tff(130,plain,
% 0.13/0.33 (~![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[129, 127])).
% 0.13/0.33 tff(131,plain,
% 0.13/0.33 (~![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[130, 127])).
% 0.13/0.33 tff(132,plain,
% 0.13/0.33 (~![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.13/0.33 tff(133,plain,
% 0.13/0.33 (~![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[132, 127])).
% 0.13/0.33 tff(134,plain,
% 0.13/0.33 (~![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[133, 127])).
% 0.13/0.33 tff(135,plain,
% 0.13/0.33 (~![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.13/0.33 tff(136,plain,
% 0.13/0.33 (~![A_27t: del, A_27w: del] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t, A_27w), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t, A_27w), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t, A_27w)))))))),
% 0.13/0.33 inference(modus_ponens,[status(thm)],[135, 127])).
% 0.13/0.33 tff(137,plain,(
% 0.13/0.33 ~(surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg, ap(c_2Ebinary__ieee_2Eulp(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__negate(A_27t!3, A_27w!2), ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t!3, A_27w!2), c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t!3, A_27w!2)))))))),
% 0.13/0.33 inference(skolemize,[status(sab)],[136])).
% 0.13/0.33 tff(138,plain,
% 0.13/0.33 ($false),
% 0.13/0.33 inference(unit_resolution,[status(thm)],[137, 126])).
% 0.13/0.33 % SZS output end Proof
%------------------------------------------------------------------------------