TSTP Solution File: SWW311+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW311+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 : Thu Sep 29 20:58:16 EDT 2022
% Result : Theorem 5.46s 4.12s
% Output : Proof 5.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW311+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 14:34:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 5.46/4.12 % SZS status Theorem
% 5.46/4.12 % SZS output start Proof
% 5.46/4.12 tff(c_Hoare__Mirabelle_Ohoare__derivs_type, type, (
% 5.46/4.12 c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o)).
% 5.46/4.12 tff(v_G_H_type, type, (
% 5.46/4.12 v_G_H: $i)).
% 5.46/4.12 tff(tptp_fun_B_G_500_type, type, (
% 5.46/4.12 tptp_fun_B_G_500: $i)).
% 5.46/4.12 tff(t_a_type, type, (
% 5.46/4.12 t_a: $i)).
% 5.46/4.12 tff(hBOOL_type, type, (
% 5.46/4.12 hBOOL: $i > $o)).
% 5.46/4.12 tff(hAPP_type, type, (
% 5.46/4.12 hAPP: ( $i * $i ) > $i)).
% 5.46/4.12 tff(c_Orderings_Oord__class_Oless__eq_type, type, (
% 5.46/4.12 c_Orderings_Oord__class_Oless__eq: $i > $i)).
% 5.46/4.12 tff(tc_fun_type, type, (
% 5.46/4.12 tc_fun: ( $i * $i ) > $i)).
% 5.46/4.12 tff(tc_HOL_Obool_type, type, (
% 5.46/4.12 tc_HOL_Obool: $i)).
% 5.46/4.12 tff(tc_Hoare__Mirabelle_Otriple_type, type, (
% 5.46/4.12 tc_Hoare__Mirabelle_Otriple: $i > $i)).
% 5.46/4.12 tff(v_ts_type, type, (
% 5.46/4.12 v_ts: $i)).
% 5.46/4.12 tff(1,plain,
% 5.46/4.12 ((~![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)))),
% 5.46/4.12 inference(rewrite,[status(thm)],[])).
% 5.46/4.12 tff(2,plain,
% 5.46/4.12 ((~![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)))),
% 5.46/4.12 inference(rewrite,[status(thm)],[])).
% 5.46/4.12 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')).
% 5.46/4.12 tff(4,plain,
% 5.46/4.12 (~![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))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[3, 2])).
% 5.46/4.12 tff(5,plain,
% 5.46/4.12 (~![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))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[4, 1])).
% 5.46/4.12 tff(6,plain,
% 5.46/4.12 (~![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))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[5, 1])).
% 5.46/4.12 tff(7,plain,
% 5.46/4.12 (~![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))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[6, 1])).
% 5.46/4.12 tff(8,plain,
% 5.46/4.12 (~![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))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[7, 1])).
% 5.46/4.12 tff(9,plain,
% 5.46/4.12 (~![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))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[8, 1])).
% 5.46/4.12 tff(10,plain,
% 5.46/4.12 (~![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))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[9, 1])).
% 5.46/4.12 tff(11,plain,
% 5.46/4.12 (~![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))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[10, 1])).
% 5.46/4.12 tff(12,plain,
% 5.46/4.12 (~![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))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[11, 1])).
% 5.46/4.12 tff(13,plain,
% 5.46/4.12 (~![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))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[12, 1])).
% 5.46/4.12 tff(14,plain,(
% 5.46/4.12 ~((~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))),
% 5.46/4.12 inference(skolemize,[status(sab)],[13])).
% 5.46/4.12 tff(15,plain,
% 5.46/4.12 (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))),
% 5.46/4.12 inference(or_elim,[status(thm)],[14])).
% 5.46/4.12 tff(16,plain,
% 5.46/4.12 (^[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)))),
% 5.46/4.12 inference(bind,[status(th)],[])).
% 5.46/4.12 tff(17,plain,
% 5.46/4.12 (![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))),
% 5.46/4.12 inference(quant_intro,[status(thm)],[16])).
% 5.46/4.12 tff(18,plain,
% 5.46/4.12 (![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))),
% 5.46/4.12 inference(rewrite,[status(thm)],[])).
% 5.46/4.12 tff(19,plain,
% 5.46/4.12 (^[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)))),
% 5.46/4.12 inference(bind,[status(th)],[])).
% 5.46/4.12 tff(20,plain,
% 5.46/4.12 (![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))),
% 5.46/4.12 inference(quant_intro,[status(thm)],[19])).
% 5.46/4.12 tff(21,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')).
% 5.46/4.12 tff(22,plain,
% 5.46/4.12 (![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))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[21, 20])).
% 5.46/4.12 tff(23,plain,
% 5.46/4.12 (![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))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[22, 18])).
% 5.46/4.12 tff(24,plain,(
% 5.46/4.12 ![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))),
% 5.46/4.12 inference(skolemize,[status(sab)],[23])).
% 5.46/4.12 tff(25,plain,
% 5.46/4.12 (![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))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[24, 17])).
% 5.46/4.12 tff(26,plain,
% 5.46/4.12 (((~![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))),
% 5.46/4.12 inference(rewrite,[status(thm)],[])).
% 5.46/4.12 tff(27,plain,
% 5.46/4.12 ((~![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))),
% 5.46/4.12 inference(quant_inst,[status(thm)],[])).
% 5.46/4.12 tff(28,plain,
% 5.46/4.12 ((~![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)),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[27, 26])).
% 5.46/4.12 tff(29,plain,
% 5.46/4.12 (c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_G_H)),
% 5.46/4.12 inference(unit_resolution,[status(thm)],[28, 25, 15])).
% 5.46/4.12 tff(30,plain,
% 5.46/4.12 (~c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_ts)),
% 5.46/4.12 inference(or_elim,[status(thm)],[14])).
% 5.46/4.12 tff(31,plain,
% 5.46/4.12 (c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts) <=> c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts)),
% 5.46/4.12 inference(rewrite,[status(thm)],[])).
% 5.46/4.12 tff(32,axiom,(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_0')).
% 5.46/4.12 tff(33,plain,
% 5.46/4.12 (c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts)),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[32, 31])).
% 5.46/4.12 tff(34,plain,
% 5.46/4.12 (^[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))))),
% 5.46/4.12 inference(bind,[status(th)],[])).
% 5.46/4.12 tff(35,plain,
% 5.46/4.12 (![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)))),
% 5.46/4.12 inference(quant_intro,[status(thm)],[34])).
% 5.46/4.12 tff(36,plain,
% 5.46/4.12 (![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)))),
% 5.46/4.12 inference(rewrite,[status(thm)],[])).
% 5.46/4.12 tff(37,plain,
% 5.46/4.12 (^[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)))))),
% 5.46/4.12 inference(bind,[status(th)],[])).
% 5.46/4.12 tff(38,plain,
% 5.46/4.12 (![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)))),
% 5.46/4.12 inference(quant_intro,[status(thm)],[37])).
% 5.46/4.12 tff(39,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')).
% 5.46/4.12 tff(40,plain,
% 5.46/4.12 (![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)))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[39, 38])).
% 5.46/4.12 tff(41,plain,
% 5.46/4.12 (![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)))),
% 5.46/4.12 inference(modus_ponens,[status(thm)],[40, 36])).
% 5.46/4.12 tff(42,plain,(
% 5.46/4.12 ![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)))),
% 5.46/4.12 inference(skolemize,[status(sab)],[41])).
% 5.46/4.12 tff(43,plain,
% 5.85/4.55 (![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)))),
% 5.85/4.55 inference(modus_ponens,[status(thm)],[42, 35])).
% 5.85/4.55 tff(44,plain,
% 5.85/4.55 (((~![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)))),
% 5.85/4.55 inference(rewrite,[status(thm)],[])).
% 5.85/4.55 tff(45,plain,
% 5.85/4.55 ((~![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)))),
% 5.85/4.55 inference(quant_inst,[status(thm)],[])).
% 5.85/4.55 tff(46,plain,
% 5.85/4.55 ((~![V_G_2: $i, V_tsa_2: $i, V_G_Ha_2: $i, T_b: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_tsa_2) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_Ha_2, V_tsa_2)) | (~c_Hoare__Mirabelle_Ohoare__derivs(T_b, V_G_2, V_G_Ha_2)))) | c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_ts) | (~c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts)) | (~c_Hoare__Mirabelle_Ohoare__derivs(t_a, B_G!500, v_G_H))),
% 5.85/4.55 inference(modus_ponens,[status(thm)],[45, 44])).
% 5.85/4.55 tff(47,plain,
% 5.85/4.55 ($false),
% 5.85/4.55 inference(unit_resolution,[status(thm)],[46, 43, 33, 30, 29])).
% 5.85/4.55 % SZS output end Proof
%------------------------------------------------------------------------------