%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW311+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:36:48 AM UTC 2025
% Result : Theorem 15.25s 15.42s
% Output : Proof 15.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW311+1 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.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 : Fri Jun 20 11:24:55 EDT 2025
% 0.13/0.34 % CPUTime :
% 15.25/15.42 % SZS status Theorem
% 15.25/15.42 % SZS output start Proof
% 15.25/15.42 tff(c_Hoare__Mirabelle_Ohoare__derivs_type, type, (
% 15.25/15.42 c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o)).
% 15.25/15.42 tff(v_G_H_type, type, (
% 15.25/15.42 v_G_H: $i)).
% 15.25/15.42 tff(tptp_fun_B_G_500_type, type, (
% 15.25/15.42 tptp_fun_B_G_500: $i)).
% 15.25/15.42 tff(t_a_type, type, (
% 15.25/15.42 t_a: $i)).
% 15.25/15.42 tff(hBOOL_type, type, (
% 15.25/15.42 hBOOL: $i > $o)).
% 15.25/15.42 tff(hAPP_type, type, (
% 15.25/15.42 hAPP: ( $i * $i ) > $i)).
% 15.25/15.42 tff(c_Orderings_Oord__class_Oless__eq_type, type, (
% 15.25/15.42 c_Orderings_Oord__class_Oless__eq: $i > $i)).
% 15.25/15.42 tff(tc_fun_type, type, (
% 15.25/15.42 tc_fun: ( $i * $i ) > $i)).
% 15.25/15.42 tff(tc_HOL_Obool_type, type, (
% 15.25/15.42 tc_HOL_Obool: $i)).
% 15.25/15.42 tff(tc_Hoare__Mirabelle_Otriple_type, type, (
% 15.25/15.42 tc_Hoare__Mirabelle_Otriple: $i > $i)).
% 15.25/15.42 tff(v_ts_type, type, (
% 15.25/15.42 v_ts: $i)).
% 15.25/15.42 tff(1,plain,
% 15.25/15.42 ((~![B_G: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G, v_ts))) <=> (~![B_G: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G, v_ts)))),
% 15.25/15.42 inference(rewrite,[status(thm)],[])).
% 15.25/15.42 tff(2,plain,
% 15.25/15.42 ((~![B_G: $i] : (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G)) => c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G, v_ts))) <=> (~![B_G: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G, v_ts)))),
% 15.25/15.42 inference(rewrite,[status(thm)],[])).
% 15.25/15.42 tff(3,axiom,(~![B_G: $i] : (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G)) => c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G, v_ts))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_1')).
% 15.25/15.42 tff(4,plain,
% 15.25/15.42 (~![B_G: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G, v_ts))),
% 15.25/15.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 15.25/15.42 tff(5,plain,
% 15.25/15.42 (~![B_G: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G, v_ts))),
% 15.25/15.42 inference(modus_ponens,[status(thm)],[4, 1])).
% 15.25/15.42 tff(6,plain,
% 15.25/15.42 (~![B_G: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G, v_ts))),
% 15.25/15.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 15.25/15.42 tff(7,plain,
% 15.25/15.42 (~![B_G: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G, v_ts))),
% 15.25/15.42 inference(modus_ponens,[status(thm)],[6, 1])).
% 15.25/15.42 tff(8,plain,(
% 15.25/15.42 ~((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G!500))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_ts))),
% 15.25/15.42 inference(skolemize,[status(sab)],[7])).
% 15.25/15.42 tff(9,plain,
% 15.25/15.42 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G!500))),
% 15.25/15.42 inference(or_elim,[status(thm)],[8])).
% 15.25/15.42 tff(10,plain,
% 15.25/15.42 (^[V_G_2: $i, V_tsa_2: $i, T_b: $i] : refl(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2)) <=> ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2)))),
% 15.25/15.42 inference(bind,[status(th)],[])).
% 15.25/15.42 tff(11,plain,
% 15.25/15.42 (![V_G_2: $i, V_tsa_2: $i, T_b: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2)) <=> ![V_G_2: $i, V_tsa_2: $i, T_b: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))),
% 15.25/15.42 inference(quant_intro,[status(thm)],[10])).
% 15.25/15.42 tff(12,plain,
% 15.25/15.42 (![V_G_2: $i, V_tsa_2: $i, T_b: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2)) <=> ![V_G_2: $i, V_tsa_2: $i, T_b: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))),
% 15.25/15.42 inference(rewrite,[status(thm)],[])).
% 15.25/15.42 tff(13,plain,
% 15.25/15.42 (^[V_G_2: $i, V_tsa_2: $i, T_b: $i] : rewrite((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2)) => c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2)) <=> ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2)))),
% 15.25/15.42 inference(bind,[status(th)],[])).
% 15.25/15.42 tff(14,plain,
% 15.25/15.42 (![V_G_2: $i, V_tsa_2: $i, T_b: $i] : (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2)) => c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2)) <=> ![V_G_2: $i, V_tsa_2: $i, T_b: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))),
% 15.25/15.42 inference(quant_intro,[status(thm)],[13])).
% 15.25/15.42 tff(15,axiom,(![V_G_2: $i, V_tsa_2: $i, T_b: $i] : (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2)) => c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_asm')).
% 15.25/15.42 tff(16,plain,
% 15.25/15.42 (![V_G_2: $i, V_tsa_2: $i, T_b: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))),
% 15.25/15.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 15.25/15.42 tff(17,plain,
% 15.25/15.42 (![V_G_2: $i, V_tsa_2: $i, T_b: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))),
% 15.25/15.42 inference(modus_ponens,[status(thm)],[16, 12])).
% 15.25/15.42 tff(18,plain,(
% 15.25/15.42 ![V_G_2: $i, V_tsa_2: $i, T_b: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))),
% 15.25/15.42 inference(skolemize,[status(sab)],[17])).
% 15.25/15.42 tff(19,plain,
% 15.25/15.42 (![V_G_2: $i, V_tsa_2: $i, T_b: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))),
% 15.25/15.42 inference(modus_ponens,[status(thm)],[18, 11])).
% 15.25/15.42 tff(20,plain,
% 15.25/15.42 (((~![V_G_2: $i, V_tsa_2: $i, T_b: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))) | ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G!500))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_G_H))) <=> ((~![V_G_2: $i, V_tsa_2: $i, T_b: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))) | (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G!500))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_G_H))),
% 15.25/15.42 inference(rewrite,[status(thm)],[])).
% 15.25/15.42 tff(21,plain,
% 15.25/15.42 ((~![V_G_2: $i, V_tsa_2: $i, T_b: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))) | ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G!500))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_G_H))),
% 15.25/15.42 inference(quant_inst,[status(thm)],[])).
% 15.25/15.42 tff(22,plain,
% 15.25/15.42 ((~![V_G_2: $i, V_tsa_2: $i, T_b: $i] : ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b), tc_HOL_Obool)), V_tsa_2), V_G_2))) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))) | (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), B_G!500))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_G_H)),
% 15.25/15.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 15.25/15.42 tff(23,plain,
% 15.25/15.42 (c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_G_H)),
% 15.25/15.42 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 15.25/15.42 tff(24,plain,
% 15.25/15.42 (~c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_ts)),
% 15.25/15.42 inference(or_elim,[status(thm)],[8])).
% 15.25/15.42 tff(25,plain,
% 15.25/15.42 (c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts) <=> c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts)),
% 15.25/15.42 inference(rewrite,[status(thm)],[])).
% 15.25/15.42 tff(26,axiom,(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_0')).
% 15.25/15.42 tff(27,plain,
% 15.25/15.42 (c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts)),
% 15.25/15.42 inference(modus_ponens,[status(thm)],[26, 25])).
% 15.25/15.42 tff(28,plain,
% 15.25/15.42 (^[V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : refl((c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2))) <=> (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2))))),
% 15.25/15.42 inference(bind,[status(th)],[])).
% 15.25/15.42 tff(29,plain,
% 15.25/15.42 (![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2))) <=> ![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))),
% 15.25/15.42 inference(quant_intro,[status(thm)],[28])).
% 15.25/15.42 tff(30,plain,
% 15.25/15.42 (![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2))) <=> ![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))),
% 15.25/15.42 inference(rewrite,[status(thm)],[])).
% 15.25/15.42 tff(31,plain,
% 15.25/15.42 (^[V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : trans(monotonicity(rewrite((c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2) => c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2)) <=> ((~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))), ((c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2) => (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2) => c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))) <=> (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2) => ((~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))))), rewrite((c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2) => ((~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)) | c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))) <=> (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))), ((c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2) => (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2) => c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))) <=> (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))))),
% 15.25/15.42 inference(bind,[status(th)],[])).
% 15.25/15.42 tff(32,plain,
% 15.25/15.42 (![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2) => (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2) => c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2))) <=> ![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))),
% 15.25/15.42 inference(quant_intro,[status(thm)],[31])).
% 15.25/15.42 tff(33,axiom,(![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2) => (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2) => c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_cut')).
% 15.25/15.42 tff(34,plain,
% 15.25/15.42 (![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))),
% 15.25/15.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 15.25/15.42 tff(35,plain,
% 15.25/15.42 (![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))),
% 15.25/15.42 inference(modus_ponens,[status(thm)],[34, 30])).
% 15.25/15.42 tff(36,plain,(
% 15.25/15.42 ![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))),
% 15.25/15.42 inference(skolemize,[status(sab)],[35])).
% 15.25/15.42 tff(37,plain,
% 15.25/15.42 (![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))),
% 15.25/15.42 inference(modus_ponens,[status(thm)],[36, 29])).
% 15.25/15.42 tff(38,plain,
% 15.25/15.42 (((~![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))) | (c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_ts) | (~c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts)) | (~c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_G_H)))) <=> ((~![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_ts) | (~c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts)) | (~c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_G_H)))),
% 15.25/15.42 inference(rewrite,[status(thm)],[])).
% 15.25/15.42 tff(39,plain,
% 15.25/15.42 ((~![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))) | (c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_ts) | (~c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts)) | (~c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_G_H)))),
% 15.70/15.87 inference(quant_inst,[status(thm)],[])).
% 15.70/15.87 tff(40,plain,
% 15.70/15.87 ((~![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_ts) | (~c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts)) | (~c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_G_H))),
% 15.70/15.87 inference(modus_ponens,[status(thm)],[39, 38])).
% 15.70/15.87 tff(41,plain,
% 15.70/15.87 ($false),
% 15.70/15.87 inference(unit_resolution,[status(thm)],[40, 37, 27, 24, 23])).
% 15.70/15.87 % SZS output end Proof
% 15.72/15.90 % E exiting
%------------------------------------------------------------------------------