%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP018+1 : TPTP v9.0.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:11:28 AM UTC 2025
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP018+1 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 18:21:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(s_type, type, (
% 0.13/0.40 s: ( $i * $i ) > $i)).
% 0.13/0.40 tff(c_2Ebinary__ieee_2Efloat__to__real_2E1_type, type, (
% 0.13/0.40 c_2Ebinary__ieee_2Efloat__to__real_2E1: $i > $i)).
% 0.13/0.40 tff(c_2Ebinary__ieee_2Efloat__negate_2E1_type, type, (
% 0.13/0.40 c_2Ebinary__ieee_2Efloat__negate_2E1: $i > $i)).
% 0.13/0.40 tff(c_2Ebinary__ieee_2Efloat__plus__min_2E1_type, type, (
% 0.13/0.40 c_2Ebinary__ieee_2Efloat__plus__min_2E1: $i > $i)).
% 0.13/0.40 tff(c_2Ebool_2Ethe__value_2E0_type, type, (
% 0.13/0.40 c_2Ebool_2Ethe__value_2E0: $i)).
% 0.13/0.40 tff(tyop_2Ebool_2Eitself_type, type, (
% 0.13/0.40 tyop_2Ebool_2Eitself: $i > $i)).
% 0.13/0.40 tff(tyop_2Epair_2Eprod_type, type, (
% 0.13/0.40 tyop_2Epair_2Eprod: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_A_27w_3_type, type, (
% 0.13/0.40 tptp_fun_A_27w_3: $i)).
% 0.13/0.40 tff(tptp_fun_A_27t_4_type, type, (
% 0.13/0.40 tptp_fun_A_27t_4: $i)).
% 0.13/0.40 tff(tyop_2Ebinary__ieee_2Efloat_type, type, (
% 0.13/0.40 tyop_2Ebinary__ieee_2Efloat: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tyop_2Erealax_2Ereal_type, type, (
% 0.13/0.40 tyop_2Erealax_2Ereal: $i)).
% 0.13/0.40 tff(c_2Erealax_2Ereal__neg_2E1_type, type, (
% 0.13/0.40 c_2Erealax_2Ereal__neg_2E1: $i > $i)).
% 0.13/0.40 tff(c_2Ebinary__ieee_2Eulp_2E1_type, type, (
% 0.13/0.40 c_2Ebinary__ieee_2Eulp_2E1: $i > $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (^[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)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(5,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')).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.40 tff(7,plain,(
% 0.13/0.40 ![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))))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ((~![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))))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (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)))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (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)))))))),
% 0.13/0.40 inference(symmetry,[status(thm)],[11])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (^[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)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(16,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')).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.40 tff(18,plain,(
% 0.13/0.40 ![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))))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[17])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 ((~![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))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (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)))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (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))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[21])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (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)))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[22])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (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)))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[23, 12])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 ((~![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)))))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(26,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')).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (~![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))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (~![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))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 25])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (~![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))))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 (~![A_27t: $i, A_27w: $i] : (s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0))))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.41 tff(31,plain,(
% 0.13/0.41 ~(s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t!4, A_27w!3), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t!4, A_27w!3)), c_2Ebool_2Ethe__value_2E0))))))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[30])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[31, 24])).
% 0.13/0.41 % SZS output end Proof
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------