TSTP Solution File: ITP018+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP018+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP018+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 03:06:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(s_type, type, (
% 0.20/0.41 s: ( $i * $i ) > $i)).
% 0.20/0.41 tff(c_2Ebinary__ieee_2Efloat__to__real_2E1_type, type, (
% 0.20/0.41 c_2Ebinary__ieee_2Efloat__to__real_2E1: $i > $i)).
% 0.20/0.41 tff(c_2Ebinary__ieee_2Efloat__negate_2E1_type, type, (
% 0.20/0.41 c_2Ebinary__ieee_2Efloat__negate_2E1: $i > $i)).
% 0.20/0.41 tff(c_2Ebinary__ieee_2Efloat__plus__min_2E1_type, type, (
% 0.20/0.41 c_2Ebinary__ieee_2Efloat__plus__min_2E1: $i > $i)).
% 0.20/0.41 tff(c_2Ebool_2Ethe__value_2E0_type, type, (
% 0.20/0.41 c_2Ebool_2Ethe__value_2E0: $i)).
% 0.20/0.41 tff(tyop_2Ebool_2Eitself_type, type, (
% 0.20/0.41 tyop_2Ebool_2Eitself: $i > $i)).
% 0.20/0.41 tff(tyop_2Epair_2Eprod_type, type, (
% 0.20/0.41 tyop_2Epair_2Eprod: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_A_27w_3_type, type, (
% 0.20/0.41 tptp_fun_A_27w_3: $i)).
% 0.20/0.41 tff(tptp_fun_A_27t_4_type, type, (
% 0.20/0.41 tptp_fun_A_27t_4: $i)).
% 0.20/0.41 tff(tyop_2Ebinary__ieee_2Efloat_type, type, (
% 0.20/0.41 tyop_2Ebinary__ieee_2Efloat: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tyop_2Erealax_2Ereal_type, type, (
% 0.20/0.41 tyop_2Erealax_2Ereal: $i)).
% 0.20/0.41 tff(c_2Erealax_2Ereal__neg_2E1_type, type, (
% 0.20/0.41 c_2Erealax_2Ereal__neg_2E1: $i > $i)).
% 0.20/0.41 tff(c_2Ebinary__ieee_2Eulp_2E1_type, type, (
% 0.20/0.41 c_2Ebinary__ieee_2Eulp_2E1: $i > $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[A_27a: $i, A_27b: $i, V0x_2E0: $i] : refl((s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0)))))) <=> (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![A_27a: $i, A_27b: $i, V0x_2E0: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0)))))) <=> ![A_27a: $i, A_27b: $i, V0x_2E0: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![A_27a: $i, A_27b: $i, V0x_2E0: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0)))))) <=> ![A_27a: $i, A_27b: $i, V0x_2E0: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,axiom,(![A_27a: $i, A_27b: $i, V0x_2E0: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Ebinary__ieee_2Efloat__to__real__negate')).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![A_27a: $i, A_27b: $i, V0x_2E0: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.41 tff(6,plain,(
% 0.20/0.41 ![A_27a: $i, A_27b: $i, V0x_2E0: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[5])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![A_27a: $i, A_27b: $i, V0x_2E0: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 ((~![A_27a: $i, A_27b: $i, V0x_2E0: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0))))))) | (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0)))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0)))))))),
% 0.20/0.41 inference(symmetry,[status(thm)],[9])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (^[A_27t: $i, A_27w: $i] : refl((s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0)))))) <=> (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0)))))) <=> ![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0)))))) <=> ![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(14,axiom,(![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Ebinary__ieee_2Eulp')).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.41 tff(16,plain,(
% 0.20/0.41 ![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[15])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 ((~![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))) | (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0)))) = c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0)))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0)))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[21, 10])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 ((~![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))))) <=> (~![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0)))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(24,axiom,(~![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Ebinary__ieee_2Eneg__ulp')).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (~![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (~![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[25, 23])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (~![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (~![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (~![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (~![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (~![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.20/0.42 tff(32,plain,(
% 0.20/0.42 ~(s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[31])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[32, 22])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------