%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SCT123+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 Jun 21 05:24:30 AM UTC 2025
% Result : Theorem 2.73s 2.93s
% Output : Proof 2.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SCT123+1 : TPTP v9.0.0. Released v5.2.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 03:47:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.73/2.93 % SZS status Theorem
% 2.73/2.93 % SZS output start Proof
% 2.73/2.93 tff(hBOOL_type, type, (
% 2.73/2.93 hBOOL: $i > $o)).
% 2.73/2.93 tff(hAPP_type, type, (
% 2.73/2.93 hAPP: ( $i * $i ) > $i)).
% 2.73/2.93 tff(c_Orderings_Obot__class_Obot_type, type, (
% 2.73/2.93 c_Orderings_Obot__class_Obot: $i > $i)).
% 2.73/2.93 tff(tc_fun_type, type, (
% 2.73/2.93 tc_fun: ( $i * $i ) > $i)).
% 2.73/2.93 tff(tc_HOL_Obool_type, type, (
% 2.73/2.93 tc_HOL_Obool: $i)).
% 2.73/2.93 tff(tc_prod_type, type, (
% 2.73/2.93 tc_prod: ( $i * $i ) > $i)).
% 2.73/2.93 tff(tc_Arrow__Order__Mirabelle_Oalt_type, type, (
% 2.73/2.93 tc_Arrow__Order__Mirabelle_Oalt: $i)).
% 2.73/2.93 tff(v_L_type, type, (
% 2.73/2.93 v_L: $i)).
% 2.73/2.93 tff(c_Set_Oinsert_type, type, (
% 2.73/2.93 c_Set_Oinsert: $i > $i)).
% 2.73/2.93 tff(c_Arrow__Order__Mirabelle_OLin_type, type, (
% 2.73/2.93 c_Arrow__Order__Mirabelle_OLin: $i)).
% 2.73/2.93 tff(c_Groups_Ominus__class_Ominus_type, type, (
% 2.73/2.93 c_Groups_Ominus__class_Ominus: $i > $i)).
% 2.73/2.93 tff(tptp_fun_B_L_2_type, type, (
% 2.73/2.93 tptp_fun_B_L_2: $i)).
% 2.73/2.93 tff(tptp_fun_B_x_39_type, type, (
% 2.73/2.93 tptp_fun_B_x_39: ( $i * $i * $i * $i * $i ) > $i)).
% 2.73/2.93 tff(c_COMBK_type, type, (
% 2.73/2.93 c_COMBK: ( $i * $i * $i ) > $i)).
% 2.73/2.93 tff(tc_Arrow__Order__Mirabelle_Oindi_type, type, (
% 2.73/2.93 tc_Arrow__Order__Mirabelle_Oindi: $i)).
% 2.73/2.93 tff(c_Orderings_Otop__class_Otop_type, type, (
% 2.73/2.93 c_Orderings_Otop__class_Otop: $i > $i)).
% 2.73/2.93 tff(c_member_type, type, (
% 2.73/2.93 c_member: $i > $i)).
% 2.73/2.93 tff(c_FuncSet_OPi_type, type, (
% 2.73/2.93 c_FuncSet_OPi: ( $i * $i * $i * $i ) > $i)).
% 2.73/2.93 tff(c_Arrow__Order__Mirabelle_OProf_type, type, (
% 2.73/2.93 c_Arrow__Order__Mirabelle_OProf: $i)).
% 2.73/2.93 tff(1,plain,
% 2.73/2.93 (^[V_A_2: $i, V_a_2: $i, T_a: $i] : refl(((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2)) <=> ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2)))),
% 2.73/2.93 inference(bind,[status(th)],[])).
% 2.73/2.93 tff(2,plain,
% 2.73/2.93 (![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2)) <=> ![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2))),
% 2.73/2.93 inference(quant_intro,[status(thm)],[1])).
% 2.73/2.93 tff(3,plain,
% 2.73/2.93 (![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2)) <=> ![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2))),
% 2.73/2.93 inference(rewrite,[status(thm)],[])).
% 2.73/2.93 tff(4,plain,
% 2.73/2.93 (^[V_A_2: $i, V_a_2: $i, T_a: $i] : rewrite((hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2)) => (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2)) <=> ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2)))),
% 2.73/2.93 inference(bind,[status(th)],[])).
% 2.73/2.93 tff(5,plain,
% 2.73/2.93 (![V_A_2: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2)) => (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2)) <=> ![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2))),
% 2.73/2.93 inference(quant_intro,[status(thm)],[4])).
% 2.73/2.93 tff(6,axiom,(![V_A_2: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2)) => (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_insert__absorb')).
% 2.73/2.93 tff(7,plain,
% 2.73/2.93 (![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[6, 5])).
% 2.73/2.93 tff(8,plain,
% 2.73/2.93 (![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.73/2.93 tff(9,plain,(
% 2.73/2.93 ![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2))),
% 2.73/2.93 inference(skolemize,[status(sab)],[8])).
% 2.73/2.93 tff(10,plain,
% 2.73/2.93 (![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[9, 2])).
% 2.73/2.94 tff(11,plain,
% 2.73/2.94 (?[B_L: $i] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L), c_Arrow__Order__Mirabelle_OLin)) <=> ?[B_L: $i] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L), c_Arrow__Order__Mirabelle_OLin))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(12,axiom,(?[B_L: $i] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L), c_Arrow__Order__Mirabelle_OLin))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_linear__alt')).
% 2.73/2.94 tff(13,plain,
% 2.73/2.94 (?[B_L: $i] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L), c_Arrow__Order__Mirabelle_OLin))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[12, 11])).
% 2.73/2.94 tff(14,plain,(
% 2.73/2.94 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), c_Arrow__Order__Mirabelle_OLin))),
% 2.73/2.94 inference(skolemize,[status(sab)],[13])).
% 2.73/2.94 tff(15,plain,
% 2.73/2.94 (((~![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2))) | ((~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), c_Arrow__Order__Mirabelle_OLin))) | (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), c_Arrow__Order__Mirabelle_OLin) = c_Arrow__Order__Mirabelle_OLin))) <=> ((~![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2))) | (~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), c_Arrow__Order__Mirabelle_OLin))) | (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), c_Arrow__Order__Mirabelle_OLin) = c_Arrow__Order__Mirabelle_OLin))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(16,plain,
% 2.73/2.94 ((~![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2))) | ((~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), c_Arrow__Order__Mirabelle_OLin))) | (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), c_Arrow__Order__Mirabelle_OLin) = c_Arrow__Order__Mirabelle_OLin))),
% 2.73/2.94 inference(quant_inst,[status(thm)],[])).
% 2.73/2.94 tff(17,plain,
% 2.73/2.94 ((~![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), V_A_2) = V_A_2))) | (~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), c_Arrow__Order__Mirabelle_OLin))) | (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), c_Arrow__Order__Mirabelle_OLin) = c_Arrow__Order__Mirabelle_OLin)),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[16, 15])).
% 2.73/2.94 tff(18,plain,
% 2.73/2.94 (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), c_Arrow__Order__Mirabelle_OLin) = c_Arrow__Order__Mirabelle_OLin),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[17, 14, 10])).
% 2.73/2.94 tff(19,plain,
% 2.73/2.94 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin)) <=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(20,axiom,(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_0')).
% 2.73/2.94 tff(21,plain,
% 2.73/2.94 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[20, 19])).
% 2.73/2.94 tff(22,plain,
% 2.73/2.94 (^[V_A_2: $i, V_a_2: $i, T_a: $i] : refl(((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2)) <=> ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2)))),
% 2.73/2.94 inference(bind,[status(th)],[])).
% 2.73/2.94 tff(23,plain,
% 2.73/2.94 (![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2)) <=> ![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2))),
% 2.73/2.94 inference(quant_intro,[status(thm)],[22])).
% 2.73/2.94 tff(24,plain,
% 2.73/2.94 (![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2)) <=> ![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(25,plain,
% 2.73/2.94 (^[V_A_2: $i, V_a_2: $i, T_a: $i] : rewrite((hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2)) => (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2)) <=> ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2)))),
% 2.73/2.94 inference(bind,[status(th)],[])).
% 2.73/2.94 tff(26,plain,
% 2.73/2.94 (![V_A_2: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2)) => (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2)) <=> ![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2))),
% 2.73/2.94 inference(quant_intro,[status(thm)],[25])).
% 2.73/2.94 tff(27,axiom,(![V_A_2: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2)) => (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_insert__Diff')).
% 2.73/2.94 tff(28,plain,
% 2.73/2.94 (![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[27, 26])).
% 2.73/2.94 tff(29,plain,
% 2.73/2.94 (![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[28, 24])).
% 2.73/2.94 tff(30,plain,(
% 2.73/2.94 ![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2))),
% 2.73/2.94 inference(skolemize,[status(sab)],[29])).
% 2.73/2.94 tff(31,plain,
% 2.73/2.94 (![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[30, 23])).
% 2.73/2.94 tff(32,plain,
% 2.73/2.94 (((~![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2))) | ((~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin))) | (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool))))) = c_Arrow__Order__Mirabelle_OLin))) <=> ((~![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2))) | (~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin))) | (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool))))) = c_Arrow__Order__Mirabelle_OLin))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(33,plain,
% 2.73/2.94 ((~![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2))) | ((~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin))) | (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool))))) = c_Arrow__Order__Mirabelle_OLin))),
% 2.73/2.94 inference(quant_inst,[status(thm)],[])).
% 2.73/2.94 tff(34,plain,
% 2.73/2.94 ((~![V_A_2: $i, V_a_2: $i, T_a: $i] : ((~hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))) | (hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a, tc_HOL_Obool)), V_A_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_a_2), c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_HOL_Obool))))) = V_A_2))) | (~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Arrow__Order__Mirabelle_OLin))) | (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool))))) = c_Arrow__Order__Mirabelle_OLin)),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[33, 32])).
% 2.73/2.94 tff(35,plain,
% 2.73/2.94 (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool))))) = c_Arrow__Order__Mirabelle_OLin),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 2.73/2.94 tff(36,plain,
% 2.73/2.94 (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), c_Arrow__Order__Mirabelle_OLin)),
% 2.73/2.94 inference(monotonicity,[status(thm)],[35])).
% 2.73/2.94 tff(37,plain,
% 2.73/2.94 (^[V_A_2: $i, V_y_2: $i, V_x_2: $i, T_a: $i] : refl((hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), V_A_2))) <=> (hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), V_A_2))))),
% 2.73/2.94 inference(bind,[status(th)],[])).
% 2.73/2.94 tff(38,plain,
% 2.73/2.94 (![V_A_2: $i, V_y_2: $i, V_x_2: $i, T_a: $i] : (hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), V_A_2))) <=> ![V_A_2: $i, V_y_2: $i, V_x_2: $i, T_a: $i] : (hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), V_A_2)))),
% 2.73/2.94 inference(quant_intro,[status(thm)],[37])).
% 2.73/2.94 tff(39,plain,
% 2.73/2.94 (![V_A_2: $i, V_y_2: $i, V_x_2: $i, T_a: $i] : (hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), V_A_2))) <=> ![V_A_2: $i, V_y_2: $i, V_x_2: $i, T_a: $i] : (hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), V_A_2)))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(40,axiom,(![V_A_2: $i, V_y_2: $i, V_x_2: $i, T_a: $i] : (hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), V_A_2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_insert__commute')).
% 2.73/2.94 tff(41,plain,
% 2.73/2.94 (![V_A_2: $i, V_y_2: $i, V_x_2: $i, T_a: $i] : (hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), V_A_2)))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[40, 39])).
% 2.73/2.94 tff(42,plain,(
% 2.73/2.94 ![V_A_2: $i, V_y_2: $i, V_x_2: $i, T_a: $i] : (hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), V_A_2)))),
% 2.73/2.94 inference(skolemize,[status(sab)],[41])).
% 2.73/2.94 tff(43,plain,
% 2.73/2.94 (![V_A_2: $i, V_y_2: $i, V_x_2: $i, T_a: $i] : (hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), V_A_2)))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[42, 38])).
% 2.73/2.94 tff(44,plain,
% 2.73/2.94 ((~![V_A_2: $i, V_y_2: $i, V_x_2: $i, T_a: $i] : (hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a), V_y_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_x_2), V_A_2)))) | (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))))),
% 2.73/2.94 inference(quant_inst,[status(thm)],[])).
% 2.73/2.94 tff(45,plain,
% 2.73/2.94 (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool))))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[44, 43])).
% 2.73/2.94 tff(46,plain,
% 2.73/2.94 (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool))))))),
% 2.73/2.94 inference(symmetry,[status(thm)],[45])).
% 2.73/2.94 tff(47,plain,
% 2.73/2.94 (hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))) = c_Arrow__Order__Mirabelle_OLin),
% 2.73/2.94 inference(transitivity,[status(thm)],[46, 36, 18])).
% 2.73/2.94 tff(48,plain,
% 2.73/2.94 (hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool))))))) = hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OLin)),
% 2.73/2.94 inference(monotonicity,[status(thm)],[47])).
% 2.73/2.94 tff(49,plain,
% 2.73/2.94 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))))) <=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OLin))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[48])).
% 2.73/2.94 tff(50,plain,
% 2.73/2.94 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OLin)) <=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool))))))))),
% 2.73/2.94 inference(symmetry,[status(thm)],[49])).
% 2.73/2.94 tff(51,plain,
% 2.73/2.94 ((~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OLin))) <=> (~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[50])).
% 2.73/2.94 tff(52,plain,
% 2.73/2.94 ((c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin))) <=> (c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin)))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(53,axiom,(c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_Prof__def')).
% 2.73/2.94 tff(54,plain,
% 2.73/2.94 (c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[53, 52])).
% 2.73/2.94 tff(55,plain,
% 2.73/2.94 (c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin)) = c_Arrow__Order__Mirabelle_OProf),
% 2.73/2.94 inference(symmetry,[status(thm)],[54])).
% 2.73/2.94 tff(56,plain,
% 2.73/2.94 (hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin))) = hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf)),
% 2.73/2.94 inference(monotonicity,[status(thm)],[55])).
% 2.73/2.94 tff(57,plain,
% 2.73/2.94 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin)))) <=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[56])).
% 2.73/2.94 tff(58,plain,
% 2.73/2.94 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf)) <=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin))))),
% 2.73/2.94 inference(symmetry,[status(thm)],[57])).
% 2.73/2.94 tff(59,plain,
% 2.73/2.94 ((~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf))) <=> (~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin)))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[58])).
% 2.73/2.94 tff(60,plain,
% 2.73/2.94 ((~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf))) <=> (~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf)))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(61,axiom,(~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_1')).
% 2.73/2.94 tff(62,plain,
% 2.73/2.94 (~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_Arrow__Order__Mirabelle_OProf))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[61, 60])).
% 2.73/2.94 tff(63,plain,
% 2.73/2.94 (~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[62, 59])).
% 2.73/2.94 tff(64,plain,
% 2.73/2.94 (^[V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : refl((hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~(hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2))), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2)), V_A_2)))))) <=> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~(hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2))), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2)), V_A_2)))))))),
% 2.73/2.94 inference(bind,[status(th)],[])).
% 2.73/2.94 tff(65,plain,
% 2.73/2.94 (![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~(hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2))), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2)), V_A_2)))))) <=> ![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~(hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2))), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2)), V_A_2))))))),
% 2.73/2.94 inference(quant_intro,[status(thm)],[64])).
% 2.73/2.94 tff(66,plain,
% 2.73/2.94 (![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2)))))) <=> ![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2))))))),
% 2.73/2.95 inference(rewrite,[status(thm)],[])).
% 2.73/2.95 tff(67,plain,
% 2.73/2.95 (^[V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : trans(monotonicity(quant_intro(proof_bind(^[B_x: $i] : rewrite((hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2)) => hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2))) <=> (hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2)))))), (![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2)) => hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2))) <=> ![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2)))))), ((![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2)) => hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2))) => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2))))) <=> (![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2)))) => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2))))))), rewrite((![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2)))) => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2))))) <=> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2))))))), ((![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2)) => hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2))) => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2))))) <=> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2))))))))),
% 2.73/2.95 inference(bind,[status(th)],[])).
% 2.73/2.95 tff(68,plain,
% 2.73/2.95 (![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2)) => hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2))) => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2))))) <=> ![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2))))))),
% 2.73/2.95 inference(quant_intro,[status(thm)],[67])).
% 2.73/2.95 tff(69,axiom,(![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2)) => hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2))) => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_funcsetI')).
% 2.73/2.95 tff(70,plain,
% 2.73/2.95 (![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2))))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[69, 68])).
% 2.73/2.95 tff(71,plain,
% 2.73/2.95 (![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, B_x)), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), B_x), V_A_2))))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[70, 66])).
% 2.73/2.95 tff(72,plain,(
% 2.73/2.95 ![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~(hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2))), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2)), V_A_2))))))),
% 2.73/2.95 inference(skolemize,[status(sab)],[71])).
% 2.73/2.95 tff(73,plain,
% 2.73/2.95 (![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~(hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2))), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2)), V_A_2))))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[72, 65])).
% 2.73/2.95 tff(74,plain,
% 2.73/2.95 (((~![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~(hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2))), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2)), V_A_2))))))) | (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin)))) | (~(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OLin)) | (~hBOOL(hAPP(hAPP(c_member(tc_Arrow__Order__Mirabelle_Oindi), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))))))) <=> ((~![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~(hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2))), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2)), V_A_2))))))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin)))) | (~(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OLin)) | (~hBOOL(hAPP(hAPP(c_member(tc_Arrow__Order__Mirabelle_Oindi), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))))))),
% 2.73/2.95 inference(rewrite,[status(thm)],[])).
% 2.73/2.95 tff(75,plain,
% 2.73/2.95 ((~![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~(hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2))), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2)), V_A_2))))))) | (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin)))) | (~(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OLin)) | (~hBOOL(hAPP(hAPP(c_member(tc_Arrow__Order__Mirabelle_Oindi), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))))))),
% 2.73/2.95 inference(quant_inst,[status(thm)],[])).
% 2.73/2.95 tff(76,plain,
% 2.73/2.95 ((~![V_B_2: $i, V_f_2: $i, T_b: $i, V_A_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) | (~(hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2))), V_B_2)) | (~hBOOL(hAPP(hAPP(c_member(T_a), tptp_fun_B_x_39(T_a, V_A_2, T_b, V_f_2, V_B_2)), V_A_2))))))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin)))) | (~(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OLin)) | (~hBOOL(hAPP(hAPP(c_member(tc_Arrow__Order__Mirabelle_Oindi), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[75, 74])).
% 2.73/2.95 tff(77,plain,
% 2.73/2.95 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L)), c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin)))) | (~(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OLin)) | (~hBOOL(hAPP(hAPP(c_member(tc_Arrow__Order__Mirabelle_Oindi), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[76, 73])).
% 2.73/2.95 tff(78,plain,
% 2.73/2.95 (~(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OLin)) | (~hBOOL(hAPP(hAPP(c_member(tc_Arrow__Order__Mirabelle_Oindi), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[77, 63])).
% 2.73/2.95 tff(79,plain,
% 2.73/2.95 ((hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OLin)) | (~hBOOL(hAPP(hAPP(c_member(tc_Arrow__Order__Mirabelle_Oindi), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))))) | (~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OLin)))),
% 2.73/2.95 inference(tautology,[status(thm)],[])).
% 2.73/2.95 tff(80,plain,
% 2.73/2.95 (~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OLin))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[79, 78])).
% 2.73/2.95 tff(81,plain,
% 2.73/2.95 (~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool))))))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[80, 51])).
% 2.73/2.95 tff(82,plain,
% 2.73/2.95 (^[V_A_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i] : refl((hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_b_2), V_A_2))) <=> ((V_a_2 = V_b_2) | hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2)))) <=> (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_b_2), V_A_2))) <=> ((V_a_2 = V_b_2) | hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2)))))),
% 2.73/2.95 inference(bind,[status(th)],[])).
% 2.73/2.95 tff(83,plain,
% 2.73/2.95 (![V_A_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_b_2), V_A_2))) <=> ((V_a_2 = V_b_2) | hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2)))) <=> ![V_A_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_b_2), V_A_2))) <=> ((V_a_2 = V_b_2) | hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))))),
% 2.73/2.95 inference(quant_intro,[status(thm)],[82])).
% 2.73/2.95 tff(84,plain,
% 2.73/2.95 (![V_A_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_b_2), V_A_2))) <=> ((V_a_2 = V_b_2) | hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2)))) <=> ![V_A_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_b_2), V_A_2))) <=> ((V_a_2 = V_b_2) | hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))))),
% 2.73/2.95 inference(rewrite,[status(thm)],[])).
% 2.73/2.95 tff(85,axiom,(![V_A_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_b_2), V_A_2))) <=> ((V_a_2 = V_b_2) | hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_insert__iff')).
% 2.73/2.95 tff(86,plain,
% 2.73/2.95 (![V_A_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_b_2), V_A_2))) <=> ((V_a_2 = V_b_2) | hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[85, 84])).
% 2.73/2.95 tff(87,plain,(
% 2.73/2.95 ![V_A_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_b_2), V_A_2))) <=> ((V_a_2 = V_b_2) | hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))))),
% 2.73/2.95 inference(skolemize,[status(sab)],[86])).
% 2.73/2.95 tff(88,plain,
% 2.73/2.95 (![V_A_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_b_2), V_A_2))) <=> ((V_a_2 = V_b_2) | hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[87, 83])).
% 2.73/2.95 tff(89,plain,
% 2.73/2.95 ((~![V_A_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), hAPP(hAPP(c_Set_Oinsert(T_a), V_b_2), V_A_2))) <=> ((V_a_2 = V_b_2) | hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), V_A_2))))) | (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))))) <=> ((hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)) = v_L) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))))))),
% 2.73/2.95 inference(quant_inst,[status(thm)],[])).
% 2.73/2.95 tff(90,plain,
% 2.73/2.95 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))))) <=> ((hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)) = v_L) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool))))))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[89, 88])).
% 2.73/2.95 tff(91,plain,
% 2.73/2.95 (^[V_Q: $i, V_P: $i, T_b: $i, T_a: $i] : refl((hAPP(c_COMBK(T_a, T_b, V_P), V_Q) = V_P) <=> (hAPP(c_COMBK(T_a, T_b, V_P), V_Q) = V_P))),
% 2.73/2.95 inference(bind,[status(th)],[])).
% 2.73/2.95 tff(92,plain,
% 2.73/2.95 (![V_Q: $i, V_P: $i, T_b: $i, T_a: $i] : (hAPP(c_COMBK(T_a, T_b, V_P), V_Q) = V_P) <=> ![V_Q: $i, V_P: $i, T_b: $i, T_a: $i] : (hAPP(c_COMBK(T_a, T_b, V_P), V_Q) = V_P)),
% 2.73/2.95 inference(quant_intro,[status(thm)],[91])).
% 2.73/2.95 tff(93,plain,
% 2.73/2.95 (![V_Q: $i, V_P: $i, T_b: $i, T_a: $i] : (hAPP(c_COMBK(T_a, T_b, V_P), V_Q) = V_P) <=> ![V_Q: $i, V_P: $i, T_b: $i, T_a: $i] : (hAPP(c_COMBK(T_a, T_b, V_P), V_Q) = V_P)),
% 2.73/2.95 inference(rewrite,[status(thm)],[])).
% 2.73/2.95 tff(94,axiom,(![V_Q: $i, V_P: $i, T_b: $i, T_a: $i] : (hAPP(c_COMBK(T_a, T_b, V_P), V_Q) = V_P)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','help_c__COMBK__1')).
% 2.73/2.95 tff(95,plain,
% 2.73/2.95 (![V_Q: $i, V_P: $i, T_b: $i, T_a: $i] : (hAPP(c_COMBK(T_a, T_b, V_P), V_Q) = V_P)),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[94, 93])).
% 2.73/2.95 tff(96,plain,(
% 2.73/2.95 ![V_Q: $i, V_P: $i, T_b: $i, T_a: $i] : (hAPP(c_COMBK(T_a, T_b, V_P), V_Q) = V_P)),
% 2.73/2.95 inference(skolemize,[status(sab)],[95])).
% 2.73/2.95 tff(97,plain,
% 2.73/2.95 (![V_Q: $i, V_P: $i, T_b: $i, T_a: $i] : (hAPP(c_COMBK(T_a, T_b, V_P), V_Q) = V_P)),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[96, 92])).
% 2.73/2.95 tff(98,plain,
% 2.73/2.95 ((~![V_Q: $i, V_P: $i, T_b: $i, T_a: $i] : (hAPP(c_COMBK(T_a, T_b, V_P), V_Q) = V_P)) | (hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)) = v_L)),
% 2.73/2.95 inference(quant_inst,[status(thm)],[])).
% 2.73/2.95 tff(99,plain,
% 2.73/2.95 (hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)) = v_L),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[98, 97])).
% 2.73/2.95 tff(100,plain,
% 2.73/2.95 (((hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)) = v_L) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))))) | (~(hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)) = v_L))),
% 2.73/2.95 inference(tautology,[status(thm)],[])).
% 2.73/2.95 tff(101,plain,
% 2.73/2.95 ((hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)) = v_L) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[100, 99])).
% 2.73/2.95 tff(102,plain,
% 2.73/2.95 ((~(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))))) <=> ((hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)) = v_L) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))))))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))))) | (~((hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin)) = v_L) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)))))))))),
% 2.83/2.99 inference(tautology,[status(thm)],[])).
% 2.83/2.99 tff(103,plain,
% 2.83/2.99 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), tptp_fun_B_x_39(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, v_L), c_Arrow__Order__Mirabelle_OLin))), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), B_L!2), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin), hAPP(hAPP(c_Set_Oinsert(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_L), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool))))))))),
% 2.83/2.99 inference(unit_resolution,[status(thm)],[102, 101, 90])).
% 2.83/2.99 tff(104,plain,
% 2.83/2.99 ($false),
% 2.83/2.99 inference(unit_resolution,[status(thm)],[103, 81])).
% 2.83/2.99 % SZS output end Proof
% 2.83/3.00 % E exiting
%------------------------------------------------------------------------------