%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA022-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 04:59:11 AM UTC 2025
% Result : Unsatisfiable 7.13s 7.36s
% Output : Proof 7.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ANA022-2 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 11:21:54 EDT 2025
% 0.13/0.35 % CPUTime :
% 7.13/7.36 % SZS status Unsatisfiable
% 7.13/7.36 % SZS output start Proof
% 7.13/7.36 tff(c_minus_type, type, (
% 7.13/7.36 c_minus: ( $i * $i * $i ) > $i)).
% 7.13/7.36 tff(t_b_type, type, (
% 7.13/7.36 t_b: $i)).
% 7.13/7.36 tff(v_g_type, type, (
% 7.13/7.36 v_g: $i > $i)).
% 7.13/7.36 tff(v_x_type, type, (
% 7.13/7.36 v_x: $i)).
% 7.13/7.36 tff(c_plus_type, type, (
% 7.13/7.36 c_plus: ( $i * $i * $i ) > $i)).
% 7.13/7.36 tff(c_uminus_type, type, (
% 7.13/7.36 c_uminus: ( $i * $i ) > $i)).
% 7.13/7.36 tff(v_f_type, type, (
% 7.13/7.36 v_f: $i > $i)).
% 7.13/7.36 tff(class_OrderedGroup_Oab__group__add_type, type, (
% 7.13/7.36 class_OrderedGroup_Oab__group__add: $i > $o)).
% 7.13/7.36 tff(class_Ring__and__Field_Oordered__idom_type, type, (
% 7.13/7.36 class_Ring__and__Field_Oordered__idom: $i > $o)).
% 7.13/7.36 tff(c_HOL_Oabs_type, type, (
% 7.13/7.36 c_HOL_Oabs: ( $i * $i ) > $i)).
% 7.13/7.36 tff(class_OrderedGroup_Olordered__ab__group__abs_type, type, (
% 7.13/7.36 class_OrderedGroup_Olordered__ab__group__abs: $i > $o)).
% 7.13/7.36 tff(c_lessequals_type, type, (
% 7.13/7.36 c_lessequals: ( $i * $i * $i ) > $o)).
% 7.13/7.36 tff(c_0_type, type, (
% 7.13/7.36 c_0: $i)).
% 7.13/7.36 tff(v_k_type, type, (
% 7.13/7.36 v_k: $i > $i)).
% 7.13/7.36 tff(class_OrderedGroup_Ocomm__monoid__add_type, type, (
% 7.13/7.36 class_OrderedGroup_Ocomm__monoid__add: $i > $o)).
% 7.13/7.36 tff(c_less_type, type, (
% 7.13/7.36 c_less: ( $i * $i * $i ) > $o)).
% 7.13/7.36 tff(class_OrderedGroup_Opordered__ab__group__add_type, type, (
% 7.13/7.36 class_OrderedGroup_Opordered__ab__group__add: $i > $o)).
% 7.13/7.36 tff(class_Orderings_Oorder_type, type, (
% 7.13/7.36 class_Orderings_Oorder: $i > $o)).
% 7.13/7.36 tff(class_LOrder_Ojoin__semilorder_type, type, (
% 7.13/7.36 class_LOrder_Ojoin__semilorder: $i > $o)).
% 7.13/7.36 tff(class_Orderings_Olinorder_type, type, (
% 7.13/7.36 class_Orderings_Olinorder: $i > $o)).
% 7.13/7.36 tff(c_Orderings_Omax_type, type, (
% 7.13/7.36 c_Orderings_Omax: ( $i * $i * $i ) > $i)).
% 7.13/7.36 tff(1,plain,
% 7.13/7.36 (^[T: $i] : refl((class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T))) <=> (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T))))),
% 7.13/7.36 inference(bind,[status(th)],[])).
% 7.13/7.36 tff(2,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T))) <=> ![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(quant_intro,[status(thm)],[1])).
% 7.13/7.36 tff(3,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T))) <=> ![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(4,plain,
% 7.13/7.36 (^[T: $i] : rewrite(((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Oab__group__add(T)) <=> (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T))))),
% 7.13/7.36 inference(bind,[status(th)],[])).
% 7.13/7.36 tff(5,plain,
% 7.13/7.36 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Oab__group__add(T)) <=> ![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(quant_intro,[status(thm)],[4])).
% 7.13/7.36 tff(6,axiom,(![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Oab__group__add(T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsrel_Ring__and__Field_Oordered__idom_4')).
% 7.13/7.36 tff(7,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 7.13/7.36 tff(8,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 7.13/7.36 tff(9,plain,(
% 7.13/7.36 ![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(skolemize,[status(sab)],[8])).
% 7.13/7.36 tff(10,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[9, 2])).
% 7.13/7.36 tff(11,plain,
% 7.13/7.36 (class_Ring__and__Field_Oordered__idom(t_b) <=> class_Ring__and__Field_Oordered__idom(t_b)),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(12,axiom,(class_Ring__and__Field_Oordered__idom(t_b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','tfree_tcs')).
% 7.13/7.36 tff(13,plain,
% 7.13/7.36 (class_Ring__and__Field_Oordered__idom(t_b)),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[12, 11])).
% 7.13/7.36 tff(14,plain,
% 7.13/7.36 (((~![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | (class_OrderedGroup_Oab__group__add(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))) <=> ((~![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | class_OrderedGroup_Oab__group__add(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(15,plain,
% 7.13/7.36 ((~![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | (class_OrderedGroup_Oab__group__add(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))),
% 7.13/7.36 inference(quant_inst,[status(thm)],[])).
% 7.13/7.36 tff(16,plain,
% 7.13/7.36 ((~![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | class_OrderedGroup_Oab__group__add(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[15, 14])).
% 7.13/7.36 tff(17,plain,
% 7.13/7.36 (class_OrderedGroup_Oab__group__add(t_b)),
% 7.13/7.36 inference(unit_resolution,[status(thm)],[16, 13, 10])).
% 7.13/7.36 tff(18,plain,
% 7.13/7.36 (^[V_c: $i, V_b: $i, V_a: $i, T_a: $i] : refl(((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a))) <=> ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a))))),
% 7.13/7.36 inference(bind,[status(th)],[])).
% 7.13/7.36 tff(19,plain,
% 7.13/7.36 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a))) <=> ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))),
% 7.13/7.36 inference(quant_intro,[status(thm)],[18])).
% 7.13/7.36 tff(20,plain,
% 7.13/7.36 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a))) <=> ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(21,axiom,(![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OrderedGroup_Ocompare__rls__2_0')).
% 7.13/7.36 tff(22,plain,
% 7.13/7.36 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[21, 20])).
% 7.13/7.36 tff(23,plain,(
% 7.13/7.36 ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))),
% 7.13/7.36 inference(skolemize,[status(sab)],[22])).
% 7.13/7.36 tff(24,plain,
% 7.13/7.36 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[23, 19])).
% 7.13/7.36 tff(25,plain,
% 7.13/7.36 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), v_f(v_x), t_b), v_g(v_x), t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), v_f(v_x), t_b), v_g(v_x), t_b)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(26,plain,
% 7.13/7.36 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), v_f(v_x), t_b), v_g(v_x), t_b)))),
% 7.13/7.36 inference(quant_inst,[status(thm)],[])).
% 7.13/7.36 tff(27,plain,
% 7.13/7.36 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), v_f(v_x), t_b), v_g(v_x), t_b))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[26, 25])).
% 7.13/7.36 tff(28,plain,
% 7.13/7.36 (c_plus(v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), v_f(v_x), t_b), v_g(v_x), t_b)),
% 7.13/7.36 inference(unit_resolution,[status(thm)],[27, 24, 17])).
% 7.13/7.36 tff(29,plain,
% 7.13/7.36 (^[V_b: $i, V_a: $i, T_a: $i] : refl(((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a))) <=> ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a))))),
% 7.13/7.36 inference(bind,[status(th)],[])).
% 7.13/7.36 tff(30,plain,
% 7.13/7.36 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))),
% 7.13/7.36 inference(quant_intro,[status(thm)],[29])).
% 7.13/7.36 tff(31,plain,
% 7.13/7.36 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(32,axiom,(![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OrderedGroup_Ominus__diff__eq_0')).
% 7.13/7.36 tff(33,plain,
% 7.13/7.36 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[32, 31])).
% 7.13/7.36 tff(34,plain,(
% 7.13/7.36 ![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))),
% 7.13/7.36 inference(skolemize,[status(sab)],[33])).
% 7.13/7.36 tff(35,plain,
% 7.13/7.36 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[34, 30])).
% 7.13/7.36 tff(36,plain,
% 7.13/7.36 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(v_f(v_x), v_g(v_x), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(v_f(v_x), v_g(v_x), t_b)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(37,plain,
% 7.13/7.36 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(v_f(v_x), v_g(v_x), t_b)))),
% 7.13/7.36 inference(quant_inst,[status(thm)],[])).
% 7.13/7.36 tff(38,plain,
% 7.13/7.36 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(v_f(v_x), v_g(v_x), t_b))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[37, 36])).
% 7.13/7.36 tff(39,plain,
% 7.13/7.36 ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(v_f(v_x), v_g(v_x), t_b))),
% 7.13/7.36 inference(unit_resolution,[status(thm)],[38, 35])).
% 7.13/7.36 tff(40,plain,
% 7.13/7.36 (c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(v_f(v_x), v_g(v_x), t_b)),
% 7.13/7.36 inference(unit_resolution,[status(thm)],[39, 17])).
% 7.13/7.36 tff(41,plain,
% 7.13/7.36 (c_minus(v_f(v_x), v_g(v_x), t_b) = c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 7.13/7.36 inference(symmetry,[status(thm)],[40])).
% 7.13/7.36 tff(42,plain,
% 7.13/7.36 (c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_HOL_Oabs(c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b)),
% 7.13/7.36 inference(monotonicity,[status(thm)],[41])).
% 7.13/7.36 tff(43,plain,
% 7.13/7.36 (c_HOL_Oabs(c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b) = c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.13/7.36 inference(symmetry,[status(thm)],[42])).
% 7.13/7.36 tff(44,plain,
% 7.13/7.36 (^[T: $i] : refl((class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T))) <=> (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T))))),
% 7.13/7.36 inference(bind,[status(th)],[])).
% 7.13/7.36 tff(45,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T))) <=> ![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(quant_intro,[status(thm)],[44])).
% 7.13/7.36 tff(46,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T))) <=> ![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(47,plain,
% 7.13/7.36 (^[T: $i] : rewrite(((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T)) <=> (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T))))),
% 7.13/7.36 inference(bind,[status(th)],[])).
% 7.13/7.36 tff(48,plain,
% 7.13/7.36 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T)) <=> ![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(quant_intro,[status(thm)],[47])).
% 7.13/7.36 tff(49,axiom,(![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsrel_Ring__and__Field_Oordered__idom_50')).
% 7.13/7.36 tff(50,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[49, 48])).
% 7.13/7.36 tff(51,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[50, 46])).
% 7.13/7.36 tff(52,plain,(
% 7.13/7.36 ![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(skolemize,[status(sab)],[51])).
% 7.13/7.36 tff(53,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[52, 45])).
% 7.13/7.36 tff(54,plain,
% 7.13/7.36 (((~![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | (class_OrderedGroup_Olordered__ab__group__abs(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))) <=> ((~![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | class_OrderedGroup_Olordered__ab__group__abs(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(55,plain,
% 7.13/7.36 ((~![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | (class_OrderedGroup_Olordered__ab__group__abs(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))),
% 7.13/7.36 inference(quant_inst,[status(thm)],[])).
% 7.13/7.36 tff(56,plain,
% 7.13/7.36 ((~![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | class_OrderedGroup_Olordered__ab__group__abs(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[55, 54])).
% 7.13/7.36 tff(57,plain,
% 7.13/7.36 (class_OrderedGroup_Olordered__ab__group__abs(t_b)),
% 7.13/7.36 inference(unit_resolution,[status(thm)],[56, 13, 53])).
% 7.13/7.36 tff(58,plain,
% 7.13/7.36 (^[V_a: $i, T_a: $i] : refl(((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a))) <=> ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a))))),
% 7.13/7.36 inference(bind,[status(th)],[])).
% 7.13/7.36 tff(59,plain,
% 7.13/7.36 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a))) <=> ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a)))),
% 7.13/7.36 inference(quant_intro,[status(thm)],[58])).
% 7.13/7.36 tff(60,plain,
% 7.13/7.36 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a))) <=> ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(61,axiom,(![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OrderedGroup_Oabs__minus__cancel_0')).
% 7.13/7.36 tff(62,plain,
% 7.13/7.36 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[61, 60])).
% 7.13/7.36 tff(63,plain,(
% 7.13/7.36 ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a)))),
% 7.13/7.36 inference(skolemize,[status(sab)],[62])).
% 7.13/7.36 tff(64,plain,
% 7.13/7.36 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[63, 59])).
% 7.13/7.36 tff(65,plain,
% 7.13/7.36 (((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a)))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (c_HOL_Oabs(c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b) = c_HOL_Oabs(c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))) <=> ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a)))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (c_HOL_Oabs(c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b) = c_HOL_Oabs(c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(66,plain,
% 7.13/7.36 ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a)))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (c_HOL_Oabs(c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b) = c_HOL_Oabs(c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 7.13/7.36 inference(quant_inst,[status(thm)],[])).
% 7.13/7.36 tff(67,plain,
% 7.13/7.36 ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(c_uminus(V_a, T_a), T_a) = c_HOL_Oabs(V_a, T_a)))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (c_HOL_Oabs(c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b) = c_HOL_Oabs(c_minus(v_g(v_x), v_f(v_x), t_b), t_b))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[66, 65])).
% 7.13/7.36 tff(68,plain,
% 7.13/7.36 (c_HOL_Oabs(c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b) = c_HOL_Oabs(c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 7.13/7.36 inference(unit_resolution,[status(thm)],[67, 64, 57])).
% 7.13/7.36 tff(69,plain,
% 7.13/7.36 (c_HOL_Oabs(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_HOL_Oabs(c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b)),
% 7.13/7.36 inference(symmetry,[status(thm)],[68])).
% 7.13/7.36 tff(70,plain,
% 7.13/7.36 (^[T: $i] : refl((class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T))) <=> (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T))))),
% 7.13/7.36 inference(bind,[status(th)],[])).
% 7.13/7.36 tff(71,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T))) <=> ![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(quant_intro,[status(thm)],[70])).
% 7.13/7.36 tff(72,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T))) <=> ![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(73,plain,
% 7.13/7.36 (^[T: $i] : rewrite(((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Ocomm__monoid__add(T)) <=> (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T))))),
% 7.13/7.36 inference(bind,[status(th)],[])).
% 7.13/7.36 tff(74,plain,
% 7.13/7.36 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Ocomm__monoid__add(T)) <=> ![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(quant_intro,[status(thm)],[73])).
% 7.13/7.36 tff(75,axiom,(![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Ocomm__monoid__add(T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsrel_Ring__and__Field_Oordered__idom_23')).
% 7.13/7.36 tff(76,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[75, 74])).
% 7.13/7.36 tff(77,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[76, 72])).
% 7.13/7.36 tff(78,plain,(
% 7.13/7.36 ![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(skolemize,[status(sab)],[77])).
% 7.13/7.36 tff(79,plain,
% 7.13/7.36 (![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[78, 71])).
% 7.13/7.36 tff(80,plain,
% 7.13/7.36 (((~![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | (class_OrderedGroup_Ocomm__monoid__add(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))) <=> ((~![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | class_OrderedGroup_Ocomm__monoid__add(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(81,plain,
% 7.13/7.36 ((~![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | (class_OrderedGroup_Ocomm__monoid__add(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))),
% 7.13/7.36 inference(quant_inst,[status(thm)],[])).
% 7.13/7.36 tff(82,plain,
% 7.13/7.36 ((~![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | class_OrderedGroup_Ocomm__monoid__add(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[81, 80])).
% 7.13/7.36 tff(83,plain,
% 7.13/7.36 (class_OrderedGroup_Ocomm__monoid__add(t_b)),
% 7.13/7.36 inference(unit_resolution,[status(thm)],[82, 13, 79])).
% 7.13/7.36 tff(84,plain,
% 7.13/7.36 (^[T_a: $i, V_y: $i] : refl(((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y)) <=> ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y)))),
% 7.13/7.36 inference(bind,[status(th)],[])).
% 7.13/7.36 tff(85,plain,
% 7.13/7.36 (![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y)) <=> ![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))),
% 7.13/7.36 inference(quant_intro,[status(thm)],[84])).
% 7.13/7.36 tff(86,plain,
% 7.13/7.36 (![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y)) <=> ![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(87,axiom,(![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0')).
% 7.13/7.36 tff(88,plain,
% 7.13/7.36 (![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[87, 86])).
% 7.13/7.36 tff(89,plain,(
% 7.13/7.36 ![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))),
% 7.13/7.36 inference(skolemize,[status(sab)],[88])).
% 7.13/7.36 tff(90,plain,
% 7.13/7.36 (![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[89, 85])).
% 7.13/7.36 tff(91,plain,
% 7.13/7.36 (((~![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))) | ((~class_OrderedGroup_Ocomm__monoid__add(t_b)) | (c_plus(c_0, v_f(v_x), t_b) = v_f(v_x)))) <=> ((~![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))) | (~class_OrderedGroup_Ocomm__monoid__add(t_b)) | (c_plus(c_0, v_f(v_x), t_b) = v_f(v_x)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(92,plain,
% 7.13/7.36 ((~![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))) | ((~class_OrderedGroup_Ocomm__monoid__add(t_b)) | (c_plus(c_0, v_f(v_x), t_b) = v_f(v_x)))),
% 7.13/7.36 inference(quant_inst,[status(thm)],[])).
% 7.13/7.36 tff(93,plain,
% 7.13/7.36 ((~![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))) | (~class_OrderedGroup_Ocomm__monoid__add(t_b)) | (c_plus(c_0, v_f(v_x), t_b) = v_f(v_x))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[92, 91])).
% 7.13/7.36 tff(94,plain,
% 7.13/7.36 (c_plus(c_0, v_f(v_x), t_b) = v_f(v_x)),
% 7.13/7.36 inference(unit_resolution,[status(thm)],[93, 90, 83])).
% 7.13/7.36 tff(95,plain,
% 7.13/7.36 (^[V_b: $i, V_a: $i, T_a: $i] : refl(((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a))) <=> ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a))))),
% 7.13/7.36 inference(bind,[status(th)],[])).
% 7.13/7.36 tff(96,plain,
% 7.13/7.36 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))),
% 7.13/7.36 inference(quant_intro,[status(thm)],[95])).
% 7.13/7.36 tff(97,plain,
% 7.13/7.36 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(98,axiom,(![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OrderedGroup_Odiff__minus__eq__add_0')).
% 7.13/7.36 tff(99,plain,
% 7.13/7.36 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[98, 97])).
% 7.13/7.36 tff(100,plain,(
% 7.13/7.36 ![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))),
% 7.13/7.36 inference(skolemize,[status(sab)],[99])).
% 7.13/7.36 tff(101,plain,
% 7.13/7.36 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[100, 96])).
% 7.13/7.36 tff(102,plain,
% 7.13/7.36 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(103,plain,
% 7.13/7.36 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b)))),
% 7.13/7.36 inference(quant_inst,[status(thm)],[])).
% 7.13/7.36 tff(104,plain,
% 7.13/7.36 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[103, 102])).
% 7.13/7.36 tff(105,plain,
% 7.13/7.36 (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b)),
% 7.13/7.36 inference(unit_resolution,[status(thm)],[104, 101, 17])).
% 7.13/7.36 tff(106,plain,
% 7.13/7.36 (^[V_a: $i, T_a: $i] : refl(((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0)) <=> ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0)))),
% 7.13/7.36 inference(bind,[status(th)],[])).
% 7.13/7.36 tff(107,plain,
% 7.13/7.36 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0)) <=> ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))),
% 7.13/7.36 inference(quant_intro,[status(thm)],[106])).
% 7.13/7.36 tff(108,plain,
% 7.13/7.36 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0)) <=> ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(109,axiom,(![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OrderedGroup_Odiff__self_0')).
% 7.13/7.36 tff(110,plain,
% 7.13/7.36 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[109, 108])).
% 7.13/7.36 tff(111,plain,(
% 7.13/7.36 ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))),
% 7.13/7.36 inference(skolemize,[status(sab)],[110])).
% 7.13/7.36 tff(112,plain,
% 7.13/7.36 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[111, 107])).
% 7.13/7.36 tff(113,plain,
% 7.13/7.36 (((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_0))) <=> ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_0))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(114,plain,
% 7.13/7.36 ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_0))),
% 7.13/7.36 inference(quant_inst,[status(thm)],[])).
% 7.13/7.36 tff(115,plain,
% 7.13/7.36 ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_0)),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[114, 113])).
% 7.13/7.36 tff(116,plain,
% 7.13/7.36 (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_0),
% 7.13/7.36 inference(unit_resolution,[status(thm)],[115, 112, 17])).
% 7.13/7.36 tff(117,plain,
% 7.13/7.36 (c_0 = c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)),
% 7.13/7.36 inference(symmetry,[status(thm)],[116])).
% 7.13/7.36 tff(118,plain,
% 7.13/7.36 (c_0 = c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b)),
% 7.13/7.36 inference(transitivity,[status(thm)],[117, 105])).
% 7.13/7.36 tff(119,plain,
% 7.13/7.36 (c_plus(c_0, v_f(v_x), t_b) = c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b)),
% 7.13/7.36 inference(monotonicity,[status(thm)],[118])).
% 7.13/7.36 tff(120,plain,
% 7.13/7.36 (c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b) = c_plus(c_0, v_f(v_x), t_b)),
% 7.13/7.36 inference(symmetry,[status(thm)],[119])).
% 7.13/7.36 tff(121,plain,
% 7.13/7.36 (c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b) = v_f(v_x)),
% 7.13/7.36 inference(transitivity,[status(thm)],[120, 94])).
% 7.13/7.36 tff(122,plain,
% 7.13/7.36 (c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b) <=> c_lessequals(v_k(v_x), v_f(v_x), t_b)),
% 7.13/7.36 inference(monotonicity,[status(thm)],[121])).
% 7.13/7.36 tff(123,plain,
% 7.13/7.36 (c_lessequals(v_k(v_x), v_f(v_x), t_b) <=> c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b)),
% 7.13/7.36 inference(symmetry,[status(thm)],[122])).
% 7.13/7.36 tff(124,plain,
% 7.13/7.36 (^[V_U: $i] : refl(c_lessequals(v_k(V_U), v_f(V_U), t_b) <=> c_lessequals(v_k(V_U), v_f(V_U), t_b))),
% 7.13/7.36 inference(bind,[status(th)],[])).
% 7.13/7.36 tff(125,plain,
% 7.13/7.36 (![V_U: $i] : c_lessequals(v_k(V_U), v_f(V_U), t_b) <=> ![V_U: $i] : c_lessequals(v_k(V_U), v_f(V_U), t_b)),
% 7.13/7.36 inference(quant_intro,[status(thm)],[124])).
% 7.13/7.36 tff(126,plain,
% 7.13/7.36 (![V_U: $i] : c_lessequals(v_k(V_U), v_f(V_U), t_b) <=> ![V_U: $i] : c_lessequals(v_k(V_U), v_f(V_U), t_b)),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(127,axiom,(![V_U: $i] : c_lessequals(v_k(V_U), v_f(V_U), t_b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 7.13/7.36 tff(128,plain,
% 7.13/7.36 (![V_U: $i] : c_lessequals(v_k(V_U), v_f(V_U), t_b)),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[127, 126])).
% 7.13/7.36 tff(129,plain,(
% 7.13/7.36 ![V_U: $i] : c_lessequals(v_k(V_U), v_f(V_U), t_b)),
% 7.13/7.36 inference(skolemize,[status(sab)],[128])).
% 7.13/7.36 tff(130,plain,
% 7.13/7.36 (![V_U: $i] : c_lessequals(v_k(V_U), v_f(V_U), t_b)),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[129, 125])).
% 7.13/7.36 tff(131,plain,
% 7.13/7.36 ((~![V_U: $i] : c_lessequals(v_k(V_U), v_f(V_U), t_b)) | c_lessequals(v_k(v_x), v_f(v_x), t_b)),
% 7.13/7.36 inference(quant_inst,[status(thm)],[])).
% 7.13/7.36 tff(132,plain,
% 7.13/7.36 (c_lessequals(v_k(v_x), v_f(v_x), t_b)),
% 7.13/7.36 inference(unit_resolution,[status(thm)],[131, 130])).
% 7.13/7.36 tff(133,plain,
% 7.13/7.36 (c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b)),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[132, 123])).
% 7.13/7.36 tff(134,plain,
% 7.13/7.36 (((~![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))) | ((~class_OrderedGroup_Ocomm__monoid__add(t_b)) | (c_plus(c_0, v_g(v_x), t_b) = v_g(v_x)))) <=> ((~![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))) | (~class_OrderedGroup_Ocomm__monoid__add(t_b)) | (c_plus(c_0, v_g(v_x), t_b) = v_g(v_x)))),
% 7.13/7.36 inference(rewrite,[status(thm)],[])).
% 7.13/7.36 tff(135,plain,
% 7.13/7.36 ((~![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))) | ((~class_OrderedGroup_Ocomm__monoid__add(t_b)) | (c_plus(c_0, v_g(v_x), t_b) = v_g(v_x)))),
% 7.13/7.36 inference(quant_inst,[status(thm)],[])).
% 7.13/7.36 tff(136,plain,
% 7.13/7.36 ((~![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))) | (~class_OrderedGroup_Ocomm__monoid__add(t_b)) | (c_plus(c_0, v_g(v_x), t_b) = v_g(v_x))),
% 7.13/7.36 inference(modus_ponens,[status(thm)],[135, 134])).
% 7.13/7.36 tff(137,plain,
% 7.13/7.36 (c_plus(c_0, v_g(v_x), t_b) = v_g(v_x)),
% 7.13/7.36 inference(unit_resolution,[status(thm)],[136, 90, 83])).
% 7.13/7.37 tff(138,plain,
% 7.13/7.37 (c_plus(c_0, v_g(v_x), t_b) = c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b)),
% 7.13/7.37 inference(monotonicity,[status(thm)],[118])).
% 7.13/7.37 tff(139,plain,
% 7.13/7.37 (c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b) = c_plus(c_0, v_g(v_x), t_b)),
% 7.13/7.37 inference(symmetry,[status(thm)],[138])).
% 7.13/7.37 tff(140,plain,
% 7.13/7.37 (c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b) = v_g(v_x)),
% 7.13/7.37 inference(transitivity,[status(thm)],[139, 137])).
% 7.13/7.37 tff(141,plain,
% 7.13/7.37 (c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) <=> c_lessequals(v_f(v_x), v_g(v_x), t_b)),
% 7.13/7.37 inference(monotonicity,[status(thm)],[121, 140])).
% 7.13/7.37 tff(142,plain,
% 7.13/7.37 (c_lessequals(v_f(v_x), v_g(v_x), t_b) <=> c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.13/7.37 inference(symmetry,[status(thm)],[141])).
% 7.13/7.37 tff(143,assumption,(~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b)), introduced(assumption)).
% 7.13/7.37 tff(144,plain,
% 7.13/7.37 (^[T: $i] : refl(((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T)) <=> ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T)))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(145,plain,
% 7.13/7.37 (![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T)) <=> ![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[144])).
% 7.13/7.37 tff(146,plain,
% 7.13/7.37 (![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T)) <=> ![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(147,axiom,(![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsrel_OrderedGroup_Olordered__ab__group__abs_1')).
% 7.13/7.37 tff(148,plain,
% 7.13/7.37 (![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[147, 146])).
% 7.13/7.37 tff(149,plain,(
% 7.13/7.37 ![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))),
% 7.13/7.37 inference(skolemize,[status(sab)],[148])).
% 7.13/7.37 tff(150,plain,
% 7.13/7.37 (![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[149, 145])).
% 7.13/7.37 tff(151,plain,
% 7.13/7.37 (((~![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | class_OrderedGroup_Opordered__ab__group__add(t_b))) <=> ((~![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | class_OrderedGroup_Opordered__ab__group__add(t_b))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(152,plain,
% 7.13/7.37 ((~![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | class_OrderedGroup_Opordered__ab__group__add(t_b))),
% 7.13/7.37 inference(quant_inst,[status(thm)],[])).
% 7.13/7.37 tff(153,plain,
% 7.13/7.37 ((~![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | class_OrderedGroup_Opordered__ab__group__add(t_b)),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[152, 151])).
% 7.13/7.37 tff(154,plain,
% 7.13/7.37 (class_OrderedGroup_Opordered__ab__group__add(t_b)),
% 7.13/7.37 inference(unit_resolution,[status(thm)],[153, 150, 57])).
% 7.13/7.37 tff(155,plain,
% 7.13/7.37 (^[V_b: $i, V_a: $i, T_a: $i] : refl((c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a))) <=> (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a))))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(156,plain,
% 7.13/7.37 (![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[155])).
% 7.13/7.37 tff(157,plain,
% 7.13/7.37 (![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(158,plain,
% 7.13/7.37 (^[V_b: $i, V_a: $i, T_a: $i] : rewrite((((~class_OrderedGroup_Opordered__ab__group__add(T_a)) | (~c_lessequals(V_a, V_b, T_a))) | c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a)) <=> (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a))))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(159,plain,
% 7.13/7.37 (![V_b: $i, V_a: $i, T_a: $i] : (((~class_OrderedGroup_Opordered__ab__group__add(T_a)) | (~c_lessequals(V_a, V_b, T_a))) | c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a)) <=> ![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[158])).
% 7.13/7.37 tff(160,axiom,(![V_b: $i, V_a: $i, T_a: $i] : (((~class_OrderedGroup_Opordered__ab__group__add(T_a)) | (~c_lessequals(V_a, V_b, T_a))) | c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OrderedGroup_Odiff__le__0__iff__le_1')).
% 7.13/7.37 tff(161,plain,
% 7.13/7.37 (![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[160, 159])).
% 7.13/7.37 tff(162,plain,
% 7.13/7.37 (![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[161, 157])).
% 7.13/7.37 tff(163,plain,(
% 7.13/7.37 ![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.13/7.37 inference(skolemize,[status(sab)],[162])).
% 7.13/7.37 tff(164,plain,
% 7.13/7.37 (![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[163, 156])).
% 7.13/7.37 tff(165,plain,
% 7.13/7.37 (((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | ((~class_OrderedGroup_Opordered__ab__group__add(t_b)) | c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) | (~c_lessequals(v_g(v_x), v_f(v_x), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) | (~c_lessequals(v_g(v_x), v_f(v_x), t_b)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(166,plain,
% 7.13/7.37 ((c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) | (~c_lessequals(v_g(v_x), v_f(v_x), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b))) <=> ((~class_OrderedGroup_Opordered__ab__group__add(t_b)) | c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) | (~c_lessequals(v_g(v_x), v_f(v_x), t_b)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(167,plain,
% 7.13/7.37 (((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) | (~c_lessequals(v_g(v_x), v_f(v_x), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | ((~class_OrderedGroup_Opordered__ab__group__add(t_b)) | c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) | (~c_lessequals(v_g(v_x), v_f(v_x), t_b))))),
% 7.13/7.37 inference(monotonicity,[status(thm)],[166])).
% 7.13/7.37 tff(168,plain,
% 7.13/7.37 (((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) | (~c_lessequals(v_g(v_x), v_f(v_x), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) | (~c_lessequals(v_g(v_x), v_f(v_x), t_b)))),
% 7.13/7.37 inference(transitivity,[status(thm)],[167, 165])).
% 7.13/7.37 tff(169,plain,
% 7.13/7.37 ((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) | (~c_lessequals(v_g(v_x), v_f(v_x), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)))),
% 7.13/7.37 inference(quant_inst,[status(thm)],[])).
% 7.13/7.37 tff(170,plain,
% 7.13/7.37 ((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) | (~c_lessequals(v_g(v_x), v_f(v_x), t_b))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[169, 168])).
% 7.13/7.37 tff(171,plain,
% 7.13/7.37 (c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) | (~c_lessequals(v_g(v_x), v_f(v_x), t_b))),
% 7.13/7.37 inference(unit_resolution,[status(thm)],[170, 164, 154])).
% 7.13/7.37 tff(172,plain,
% 7.13/7.37 (~c_lessequals(v_g(v_x), v_f(v_x), t_b)),
% 7.13/7.37 inference(unit_resolution,[status(thm)],[171, 143])).
% 7.13/7.37 tff(173,plain,
% 7.13/7.37 (^[T: $i] : refl((class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T))) <=> (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T))))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(174,plain,
% 7.13/7.37 (![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T))) <=> ![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[173])).
% 7.13/7.37 tff(175,plain,
% 7.13/7.37 (![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T))) <=> ![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(176,plain,
% 7.13/7.37 (^[T: $i] : rewrite(((~class_Ring__and__Field_Oordered__idom(T)) | class_LOrder_Ojoin__semilorder(T)) <=> (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T))))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(177,plain,
% 7.13/7.37 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_LOrder_Ojoin__semilorder(T)) <=> ![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[176])).
% 7.13/7.37 tff(178,axiom,(![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_LOrder_Ojoin__semilorder(T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsrel_Ring__and__Field_Oordered__idom_35')).
% 7.13/7.37 tff(179,plain,
% 7.13/7.37 (![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[178, 177])).
% 7.13/7.37 tff(180,plain,
% 7.13/7.37 (![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[179, 175])).
% 7.13/7.37 tff(181,plain,(
% 7.13/7.37 ![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.37 inference(skolemize,[status(sab)],[180])).
% 7.13/7.37 tff(182,plain,
% 7.13/7.37 (![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[181, 174])).
% 7.13/7.37 tff(183,plain,
% 7.13/7.37 (((~![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | (class_LOrder_Ojoin__semilorder(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))) <=> ((~![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | class_LOrder_Ojoin__semilorder(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(184,plain,
% 7.13/7.37 ((~![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | (class_LOrder_Ojoin__semilorder(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))),
% 7.13/7.37 inference(quant_inst,[status(thm)],[])).
% 7.13/7.37 tff(185,plain,
% 7.13/7.37 ((~![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))) | class_LOrder_Ojoin__semilorder(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[184, 183])).
% 7.13/7.37 tff(186,plain,
% 7.13/7.37 (class_LOrder_Ojoin__semilorder(t_b)),
% 7.13/7.37 inference(unit_resolution,[status(thm)],[185, 13, 182])).
% 7.13/7.37 tff(187,plain,
% 7.13/7.37 (^[T: $i] : refl((class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T))) <=> (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T))))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(188,plain,
% 7.13/7.37 (![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T))) <=> ![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[187])).
% 7.13/7.37 tff(189,plain,
% 7.13/7.37 (![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T))) <=> ![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(190,plain,
% 7.13/7.37 (^[T: $i] : rewrite(((~class_LOrder_Ojoin__semilorder(T)) | class_Orderings_Oorder(T)) <=> (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T))))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(191,plain,
% 7.13/7.37 (![T: $i] : ((~class_LOrder_Ojoin__semilorder(T)) | class_Orderings_Oorder(T)) <=> ![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[190])).
% 7.13/7.37 tff(192,axiom,(![T: $i] : ((~class_LOrder_Ojoin__semilorder(T)) | class_Orderings_Oorder(T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsrel_LOrder_Ojoin__semilorder_1')).
% 7.13/7.37 tff(193,plain,
% 7.13/7.37 (![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[192, 191])).
% 7.13/7.37 tff(194,plain,
% 7.13/7.37 (![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[193, 189])).
% 7.13/7.37 tff(195,plain,(
% 7.13/7.37 ![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 7.13/7.37 inference(skolemize,[status(sab)],[194])).
% 7.13/7.37 tff(196,plain,
% 7.13/7.37 (![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[195, 188])).
% 7.13/7.37 tff(197,plain,
% 7.13/7.37 (((~![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))) | (class_Orderings_Oorder(t_b) | (~class_LOrder_Ojoin__semilorder(t_b)))) <=> ((~![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))) | class_Orderings_Oorder(t_b) | (~class_LOrder_Ojoin__semilorder(t_b)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(198,plain,
% 7.13/7.37 ((~![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))) | (class_Orderings_Oorder(t_b) | (~class_LOrder_Ojoin__semilorder(t_b)))),
% 7.13/7.37 inference(quant_inst,[status(thm)],[])).
% 7.13/7.37 tff(199,plain,
% 7.13/7.37 ((~![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))) | class_Orderings_Oorder(t_b) | (~class_LOrder_Ojoin__semilorder(t_b))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[198, 197])).
% 7.13/7.37 tff(200,plain,
% 7.13/7.37 (class_Orderings_Oorder(t_b)),
% 7.13/7.37 inference(unit_resolution,[status(thm)],[199, 196, 186])).
% 7.13/7.37 tff(201,plain,
% 7.13/7.37 (^[V_x: $i, T_a: $i, V_y: $i] : refl((c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a))) <=> (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a))))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(202,plain,
% 7.13/7.37 (![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a))) <=> ![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[201])).
% 7.13/7.37 tff(203,plain,
% 7.13/7.37 (![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a))) <=> ![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(204,plain,
% 7.13/7.37 (^[V_x: $i, T_a: $i, V_y: $i] : rewrite((((~class_Orderings_Oorder(T_a)) | (~c_less(V_x, V_y, T_a))) | c_lessequals(V_x, V_y, T_a)) <=> (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a))))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(205,plain,
% 7.13/7.37 (![V_x: $i, T_a: $i, V_y: $i] : (((~class_Orderings_Oorder(T_a)) | (~c_less(V_x, V_y, T_a))) | c_lessequals(V_x, V_y, T_a)) <=> ![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[204])).
% 7.13/7.37 tff(206,axiom,(![V_x: $i, T_a: $i, V_y: $i] : (((~class_Orderings_Oorder(T_a)) | (~c_less(V_x, V_y, T_a))) | c_lessequals(V_x, V_y, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Orderings_Oorder__less__imp__le_0')).
% 7.13/7.37 tff(207,plain,
% 7.13/7.37 (![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[206, 205])).
% 7.13/7.37 tff(208,plain,
% 7.13/7.37 (![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[207, 203])).
% 7.13/7.37 tff(209,plain,(
% 7.13/7.37 ![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.13/7.37 inference(skolemize,[status(sab)],[208])).
% 7.13/7.37 tff(210,plain,
% 7.13/7.37 (![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[209, 202])).
% 7.13/7.37 tff(211,plain,
% 7.13/7.37 (((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | ((~class_Orderings_Oorder(t_b)) | c_lessequals(v_g(v_x), v_f(v_x), t_b) | (~c_less(v_g(v_x), v_f(v_x), t_b)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | (~class_Orderings_Oorder(t_b)) | c_lessequals(v_g(v_x), v_f(v_x), t_b) | (~c_less(v_g(v_x), v_f(v_x), t_b)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(212,plain,
% 7.13/7.37 ((c_lessequals(v_g(v_x), v_f(v_x), t_b) | (~c_less(v_g(v_x), v_f(v_x), t_b)) | (~class_Orderings_Oorder(t_b))) <=> ((~class_Orderings_Oorder(t_b)) | c_lessequals(v_g(v_x), v_f(v_x), t_b) | (~c_less(v_g(v_x), v_f(v_x), t_b)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(213,plain,
% 7.13/7.37 (((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(v_g(v_x), v_f(v_x), t_b) | (~c_less(v_g(v_x), v_f(v_x), t_b)) | (~class_Orderings_Oorder(t_b)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | ((~class_Orderings_Oorder(t_b)) | c_lessequals(v_g(v_x), v_f(v_x), t_b) | (~c_less(v_g(v_x), v_f(v_x), t_b))))),
% 7.13/7.37 inference(monotonicity,[status(thm)],[212])).
% 7.13/7.37 tff(214,plain,
% 7.13/7.37 (((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(v_g(v_x), v_f(v_x), t_b) | (~c_less(v_g(v_x), v_f(v_x), t_b)) | (~class_Orderings_Oorder(t_b)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | (~class_Orderings_Oorder(t_b)) | c_lessequals(v_g(v_x), v_f(v_x), t_b) | (~c_less(v_g(v_x), v_f(v_x), t_b)))),
% 7.13/7.37 inference(transitivity,[status(thm)],[213, 211])).
% 7.13/7.37 tff(215,plain,
% 7.13/7.37 ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(v_g(v_x), v_f(v_x), t_b) | (~c_less(v_g(v_x), v_f(v_x), t_b)) | (~class_Orderings_Oorder(t_b)))),
% 7.13/7.37 inference(quant_inst,[status(thm)],[])).
% 7.13/7.37 tff(216,plain,
% 7.13/7.37 ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | (~class_Orderings_Oorder(t_b)) | c_lessequals(v_g(v_x), v_f(v_x), t_b) | (~c_less(v_g(v_x), v_f(v_x), t_b))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[215, 214])).
% 7.13/7.37 tff(217,plain,
% 7.13/7.37 (~c_less(v_g(v_x), v_f(v_x), t_b)),
% 7.13/7.37 inference(unit_resolution,[status(thm)],[216, 210, 200, 172])).
% 7.13/7.37 tff(218,plain,
% 7.13/7.37 (^[T: $i] : refl(((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T)) <=> ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T)))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(219,plain,
% 7.13/7.37 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T)) <=> ![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[218])).
% 7.13/7.37 tff(220,plain,
% 7.13/7.37 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T)) <=> ![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(221,axiom,(![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsrel_Ring__and__Field_Oordered__idom_33')).
% 7.13/7.37 tff(222,plain,
% 7.13/7.37 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[221, 220])).
% 7.13/7.37 tff(223,plain,(
% 7.13/7.37 ![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))),
% 7.13/7.37 inference(skolemize,[status(sab)],[222])).
% 7.13/7.37 tff(224,plain,
% 7.13/7.37 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[223, 219])).
% 7.13/7.37 tff(225,plain,
% 7.13/7.37 (((~![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))) | (class_Orderings_Olinorder(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))) <=> ((~![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))) | class_Orderings_Olinorder(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(226,plain,
% 7.13/7.37 (((~class_Ring__and__Field_Oordered__idom(t_b)) | class_Orderings_Olinorder(t_b)) <=> (class_Orderings_Olinorder(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(227,plain,
% 7.13/7.37 (((~![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))) | ((~class_Ring__and__Field_Oordered__idom(t_b)) | class_Orderings_Olinorder(t_b))) <=> ((~![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))) | (class_Orderings_Olinorder(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b))))),
% 7.13/7.37 inference(monotonicity,[status(thm)],[226])).
% 7.13/7.37 tff(228,plain,
% 7.13/7.37 (((~![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))) | ((~class_Ring__and__Field_Oordered__idom(t_b)) | class_Orderings_Olinorder(t_b))) <=> ((~![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))) | class_Orderings_Olinorder(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b)))),
% 7.13/7.37 inference(transitivity,[status(thm)],[227, 225])).
% 7.13/7.37 tff(229,plain,
% 7.13/7.37 ((~![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))) | ((~class_Ring__and__Field_Oordered__idom(t_b)) | class_Orderings_Olinorder(t_b))),
% 7.13/7.37 inference(quant_inst,[status(thm)],[])).
% 7.13/7.37 tff(230,plain,
% 7.13/7.37 ((~![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))) | class_Orderings_Olinorder(t_b) | (~class_Ring__and__Field_Oordered__idom(t_b))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[229, 228])).
% 7.13/7.37 tff(231,plain,
% 7.13/7.37 (class_Orderings_Olinorder(t_b)),
% 7.13/7.37 inference(unit_resolution,[status(thm)],[230, 13, 224])).
% 7.13/7.37 tff(232,plain,
% 7.13/7.37 (^[V_x: $i, T_a: $i, V_y: $i] : refl((c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a))) <=> (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a))))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(233,plain,
% 7.13/7.37 (![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a))) <=> ![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[232])).
% 7.13/7.37 tff(234,plain,
% 7.13/7.37 (![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a))) <=> ![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(235,plain,
% 7.13/7.37 (^[V_x: $i, T_a: $i, V_y: $i] : rewrite((((~class_Orderings_Olinorder(T_a)) | c_less(V_y, V_x, T_a)) | c_lessequals(V_x, V_y, T_a)) <=> (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a))))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(236,plain,
% 7.13/7.37 (![V_x: $i, T_a: $i, V_y: $i] : (((~class_Orderings_Olinorder(T_a)) | c_less(V_y, V_x, T_a)) | c_lessequals(V_x, V_y, T_a)) <=> ![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[235])).
% 7.13/7.37 tff(237,axiom,(![V_x: $i, T_a: $i, V_y: $i] : (((~class_Orderings_Olinorder(T_a)) | c_less(V_y, V_x, T_a)) | c_lessequals(V_x, V_y, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Orderings_Olinorder__not__le_0')).
% 7.13/7.37 tff(238,plain,
% 7.13/7.37 (![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[237, 236])).
% 7.13/7.37 tff(239,plain,
% 7.13/7.37 (![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[238, 234])).
% 7.13/7.37 tff(240,plain,(
% 7.13/7.37 ![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))),
% 7.13/7.37 inference(skolemize,[status(sab)],[239])).
% 7.13/7.37 tff(241,plain,
% 7.13/7.37 (![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[240, 233])).
% 7.13/7.37 tff(242,plain,
% 7.13/7.37 (((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | ((~class_Orderings_Olinorder(t_b)) | c_lessequals(v_f(v_x), v_g(v_x), t_b) | c_less(v_g(v_x), v_f(v_x), t_b))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | (~class_Orderings_Olinorder(t_b)) | c_lessequals(v_f(v_x), v_g(v_x), t_b) | c_less(v_g(v_x), v_f(v_x), t_b))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(243,plain,
% 7.13/7.37 ((c_lessequals(v_f(v_x), v_g(v_x), t_b) | c_less(v_g(v_x), v_f(v_x), t_b) | (~class_Orderings_Olinorder(t_b))) <=> ((~class_Orderings_Olinorder(t_b)) | c_lessequals(v_f(v_x), v_g(v_x), t_b) | c_less(v_g(v_x), v_f(v_x), t_b))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(244,plain,
% 7.13/7.37 (((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | (c_lessequals(v_f(v_x), v_g(v_x), t_b) | c_less(v_g(v_x), v_f(v_x), t_b) | (~class_Orderings_Olinorder(t_b)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | ((~class_Orderings_Olinorder(t_b)) | c_lessequals(v_f(v_x), v_g(v_x), t_b) | c_less(v_g(v_x), v_f(v_x), t_b)))),
% 7.13/7.37 inference(monotonicity,[status(thm)],[243])).
% 7.13/7.37 tff(245,plain,
% 7.13/7.37 (((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | (c_lessequals(v_f(v_x), v_g(v_x), t_b) | c_less(v_g(v_x), v_f(v_x), t_b) | (~class_Orderings_Olinorder(t_b)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | (~class_Orderings_Olinorder(t_b)) | c_lessequals(v_f(v_x), v_g(v_x), t_b) | c_less(v_g(v_x), v_f(v_x), t_b))),
% 7.13/7.37 inference(transitivity,[status(thm)],[244, 242])).
% 7.13/7.37 tff(246,plain,
% 7.13/7.37 ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | (c_lessequals(v_f(v_x), v_g(v_x), t_b) | c_less(v_g(v_x), v_f(v_x), t_b) | (~class_Orderings_Olinorder(t_b)))),
% 7.13/7.37 inference(quant_inst,[status(thm)],[])).
% 7.13/7.37 tff(247,plain,
% 7.13/7.37 ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | (~class_Orderings_Olinorder(t_b)) | c_lessequals(v_f(v_x), v_g(v_x), t_b) | c_less(v_g(v_x), v_f(v_x), t_b)),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[246, 245])).
% 7.13/7.37 tff(248,plain,
% 7.13/7.37 (c_lessequals(v_f(v_x), v_g(v_x), t_b)),
% 7.13/7.37 inference(unit_resolution,[status(thm)],[247, 241, 231, 217])).
% 7.13/7.37 tff(249,plain,
% 7.13/7.37 (c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[248, 142])).
% 7.13/7.37 tff(250,plain,
% 7.13/7.37 (c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)),
% 7.13/7.37 inference(symmetry,[status(thm)],[105])).
% 7.13/7.37 tff(251,plain,
% 7.13/7.37 (c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b) = c_0),
% 7.13/7.37 inference(transitivity,[status(thm)],[250, 116])).
% 7.13/7.37 tff(252,plain,
% 7.13/7.37 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), v_f(v_x), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), v_f(v_x), t_b)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(253,plain,
% 7.13/7.37 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), v_f(v_x), t_b)))),
% 7.13/7.37 inference(quant_inst,[status(thm)],[])).
% 7.13/7.37 tff(254,plain,
% 7.13/7.37 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), v_f(v_x), t_b))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[253, 252])).
% 7.13/7.37 tff(255,plain,
% 7.13/7.37 ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), v_f(v_x), t_b))),
% 7.13/7.37 inference(unit_resolution,[status(thm)],[254, 35])).
% 7.13/7.37 tff(256,plain,
% 7.13/7.37 (c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), v_f(v_x), t_b)),
% 7.13/7.37 inference(unit_resolution,[status(thm)],[255, 17])).
% 7.13/7.37 tff(257,plain,
% 7.13/7.37 (((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_f(v_x), v_g(v_x), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_f(v_x), v_g(v_x), t_b)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(258,plain,
% 7.13/7.37 ((c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b) | (~c_lessequals(v_f(v_x), v_g(v_x), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b))) <=> (c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_f(v_x), v_g(v_x), t_b)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(259,plain,
% 7.13/7.37 (((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b) | (~c_lessequals(v_f(v_x), v_g(v_x), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_f(v_x), v_g(v_x), t_b))))),
% 7.13/7.37 inference(monotonicity,[status(thm)],[258])).
% 7.13/7.37 tff(260,plain,
% 7.13/7.37 (((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b) | (~c_lessequals(v_f(v_x), v_g(v_x), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_f(v_x), v_g(v_x), t_b)))),
% 7.13/7.37 inference(transitivity,[status(thm)],[259, 257])).
% 7.13/7.37 tff(261,plain,
% 7.13/7.37 ((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b) | (~c_lessequals(v_f(v_x), v_g(v_x), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)))),
% 7.13/7.37 inference(quant_inst,[status(thm)],[])).
% 7.13/7.37 tff(262,plain,
% 7.13/7.37 ((~![V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), c_0, T_a) | (~c_lessequals(V_a, V_b, T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_f(v_x), v_g(v_x), t_b))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[261, 260])).
% 7.13/7.37 tff(263,plain,
% 7.13/7.37 (c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_f(v_x), v_g(v_x), t_b))),
% 7.13/7.37 inference(unit_resolution,[status(thm)],[262, 164])).
% 7.13/7.37 tff(264,plain,
% 7.13/7.37 (c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b) | (~c_lessequals(v_f(v_x), v_g(v_x), t_b))),
% 7.13/7.37 inference(unit_resolution,[status(thm)],[263, 154])).
% 7.13/7.37 tff(265,plain,
% 7.13/7.37 (c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b)),
% 7.13/7.37 inference(unit_resolution,[status(thm)],[264, 248])).
% 7.13/7.37 tff(266,plain,
% 7.13/7.37 (^[V_a: $i, T_a: $i] : refl(((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a))) <=> ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a))))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(267,plain,
% 7.13/7.37 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a))) <=> ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[266])).
% 7.13/7.37 tff(268,plain,
% 7.13/7.37 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a))) <=> ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))),
% 7.13/7.37 inference(rewrite,[status(thm)],[])).
% 7.13/7.37 tff(269,plain,
% 7.13/7.37 (^[V_a: $i, T_a: $i] : rewrite((((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (~c_lessequals(V_a, c_0, T_a))) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a))) <=> ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a))))),
% 7.13/7.37 inference(bind,[status(th)],[])).
% 7.13/7.37 tff(270,plain,
% 7.13/7.37 (![V_a: $i, T_a: $i] : (((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (~c_lessequals(V_a, c_0, T_a))) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a))) <=> ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))),
% 7.13/7.37 inference(quant_intro,[status(thm)],[269])).
% 7.13/7.37 tff(271,axiom,(![V_a: $i, T_a: $i] : (((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (~c_lessequals(V_a, c_0, T_a))) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OrderedGroup_Oabs__of__nonpos_0')).
% 7.13/7.37 tff(272,plain,
% 7.13/7.37 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[271, 270])).
% 7.13/7.37 tff(273,plain,
% 7.13/7.37 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[272, 268])).
% 7.13/7.37 tff(274,plain,(
% 7.13/7.37 ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))),
% 7.13/7.37 inference(skolemize,[status(sab)],[273])).
% 7.13/7.37 tff(275,plain,
% 7.13/7.37 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))),
% 7.13/7.37 inference(modus_ponens,[status(thm)],[274, 267])).
% 7.13/7.37 tff(276,plain,
% 7.13/7.37 (((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b)))) <=> ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b)))),
% 7.13/7.38 inference(rewrite,[status(thm)],[])).
% 7.13/7.38 tff(277,plain,
% 7.13/7.38 ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b)))),
% 7.13/7.38 inference(quant_inst,[status(thm)],[])).
% 7.13/7.38 tff(278,plain,
% 7.13/7.38 ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b))),
% 7.13/7.38 inference(modus_ponens,[status(thm)],[277, 276])).
% 7.13/7.38 tff(279,plain,
% 7.13/7.38 ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b))),
% 7.13/7.38 inference(unit_resolution,[status(thm)],[278, 275])).
% 7.13/7.38 tff(280,plain,
% 7.13/7.38 ((c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b))),
% 7.13/7.38 inference(unit_resolution,[status(thm)],[279, 57])).
% 7.13/7.38 tff(281,plain,
% 7.13/7.38 (c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.13/7.38 inference(unit_resolution,[status(thm)],[280, 265])).
% 7.13/7.38 tff(282,plain,
% 7.13/7.38 (c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), v_f(v_x), t_b)),
% 7.13/7.38 inference(transitivity,[status(thm)],[281, 256])).
% 7.13/7.38 tff(283,plain,
% 7.13/7.38 (c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) <=> c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b)),
% 7.13/7.38 inference(monotonicity,[status(thm)],[282, 251])).
% 7.13/7.38 tff(284,plain,
% 7.13/7.38 (c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) <=> c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.13/7.38 inference(symmetry,[status(thm)],[283])).
% 7.13/7.38 tff(285,plain,
% 7.13/7.38 ((~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b)) <=> (~c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 7.13/7.38 inference(monotonicity,[status(thm)],[284])).
% 7.13/7.38 tff(286,plain,
% 7.13/7.38 (~c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.13/7.38 inference(modus_ponens,[status(thm)],[143, 285])).
% 7.13/7.38 tff(287,plain,
% 7.13/7.38 (^[V_a: $i, T_a: $i] : refl(((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a)) <=> ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a)))),
% 7.13/7.38 inference(bind,[status(th)],[])).
% 7.13/7.38 tff(288,plain,
% 7.13/7.38 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a)) <=> ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a))),
% 7.13/7.38 inference(quant_intro,[status(thm)],[287])).
% 7.13/7.38 tff(289,plain,
% 7.13/7.38 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a)) <=> ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a))),
% 7.13/7.38 inference(rewrite,[status(thm)],[])).
% 7.13/7.38 tff(290,axiom,(![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OrderedGroup_Oabs__ge__zero_0')).
% 7.13/7.38 tff(291,plain,
% 7.13/7.38 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a))),
% 7.13/7.38 inference(modus_ponens,[status(thm)],[290, 289])).
% 7.13/7.38 tff(292,plain,(
% 7.13/7.38 ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a))),
% 7.13/7.38 inference(skolemize,[status(sab)],[291])).
% 7.13/7.38 tff(293,plain,
% 7.13/7.38 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a))),
% 7.13/7.38 inference(modus_ponens,[status(thm)],[292, 288])).
% 7.13/7.38 tff(294,plain,
% 7.13/7.38 (((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b))) <=> ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b))),
% 7.13/7.38 inference(rewrite,[status(thm)],[])).
% 7.13/7.38 tff(295,plain,
% 7.13/7.38 ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b))),
% 7.13/7.38 inference(quant_inst,[status(thm)],[])).
% 7.13/7.38 tff(296,plain,
% 7.13/7.38 ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.13/7.38 inference(modus_ponens,[status(thm)],[295, 294])).
% 7.13/7.38 tff(297,plain,
% 7.13/7.38 ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.13/7.38 inference(unit_resolution,[status(thm)],[296, 293])).
% 7.13/7.38 tff(298,plain,
% 7.13/7.38 (c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.13/7.38 inference(unit_resolution,[status(thm)],[297, 57])).
% 7.13/7.38 tff(299,plain,
% 7.13/7.38 (^[T_b: $i, V_x: $i, V_z: $i, V_y: $i] : refl((c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b))) <=> (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b))))),
% 7.13/7.38 inference(bind,[status(th)],[])).
% 7.13/7.38 tff(300,plain,
% 7.13/7.38 (![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b))) <=> ![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))),
% 7.13/7.38 inference(quant_intro,[status(thm)],[299])).
% 7.13/7.38 tff(301,plain,
% 7.13/7.38 (![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b))) <=> ![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))),
% 7.13/7.38 inference(rewrite,[status(thm)],[])).
% 7.13/7.38 tff(302,plain,
% 7.13/7.38 (^[T_b: $i, V_x: $i, V_z: $i, V_y: $i] : trans(monotonicity(rewrite((((~class_Orderings_Olinorder(T_b)) | (~c_lessequals(V_y, V_z, T_b))) | (~c_lessequals(V_x, V_z, T_b))) <=> ((~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))), (((((~class_Orderings_Olinorder(T_b)) | (~c_lessequals(V_y, V_z, T_b))) | (~c_lessequals(V_x, V_z, T_b))) | c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b)) <=> (((~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b))) | c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b)))), rewrite((((~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b))) | c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b)) <=> (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))), (((((~class_Orderings_Olinorder(T_b)) | (~c_lessequals(V_y, V_z, T_b))) | (~c_lessequals(V_x, V_z, T_b))) | c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b)) <=> (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))))),
% 7.13/7.38 inference(bind,[status(th)],[])).
% 7.13/7.38 tff(303,plain,
% 7.13/7.38 (![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : ((((~class_Orderings_Olinorder(T_b)) | (~c_lessequals(V_y, V_z, T_b))) | (~c_lessequals(V_x, V_z, T_b))) | c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b)) <=> ![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))),
% 7.13/7.38 inference(quant_intro,[status(thm)],[302])).
% 7.13/7.38 tff(304,axiom,(![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : ((((~class_Orderings_Olinorder(T_b)) | (~c_lessequals(V_y, V_z, T_b))) | (~c_lessequals(V_x, V_z, T_b))) | c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2')).
% 7.13/7.38 tff(305,plain,
% 7.13/7.38 (![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))),
% 7.13/7.38 inference(modus_ponens,[status(thm)],[304, 303])).
% 7.13/7.38 tff(306,plain,
% 7.13/7.38 (![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))),
% 7.13/7.38 inference(modus_ponens,[status(thm)],[305, 301])).
% 7.13/7.38 tff(307,plain,(
% 7.13/7.38 ![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))),
% 7.13/7.38 inference(skolemize,[status(sab)],[306])).
% 7.13/7.38 tff(308,plain,
% 7.13/7.38 (![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))),
% 7.13/7.38 inference(modus_ponens,[status(thm)],[307, 300])).
% 7.13/7.38 tff(309,plain,
% 7.13/7.38 ((~c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) <=> (~c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b))),
% 7.13/7.38 inference(rewrite,[status(thm)],[])).
% 7.13/7.38 tff(310,axiom,(~c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 7.13/7.38 tff(311,plain,
% 7.13/7.38 (~c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.13/7.38 inference(modus_ponens,[status(thm)],[310, 309])).
% 7.13/7.38 tff(312,plain,
% 7.13/7.38 (((~![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))) | (c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~class_Orderings_Olinorder(t_b)) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))) <=> ((~![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))) | c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~class_Orderings_Olinorder(t_b)) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))),
% 7.22/7.38 inference(rewrite,[status(thm)],[])).
% 7.22/7.38 tff(313,plain,
% 7.22/7.38 ((c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~class_Orderings_Olinorder(t_b))) <=> (c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~class_Orderings_Olinorder(t_b)) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))),
% 7.22/7.38 inference(rewrite,[status(thm)],[])).
% 7.22/7.38 tff(314,plain,
% 7.22/7.38 (((~![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))) | (c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~class_Orderings_Olinorder(t_b)))) <=> ((~![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))) | (c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~class_Orderings_Olinorder(t_b)) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b))))),
% 7.22/7.38 inference(monotonicity,[status(thm)],[313])).
% 7.22/7.38 tff(315,plain,
% 7.22/7.38 (((~![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))) | (c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~class_Orderings_Olinorder(t_b)))) <=> ((~![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))) | c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~class_Orderings_Olinorder(t_b)) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))),
% 7.22/7.38 inference(transitivity,[status(thm)],[314, 312])).
% 7.22/7.38 tff(316,plain,
% 7.22/7.38 ((~![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))) | (c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~class_Orderings_Olinorder(t_b)))),
% 7.22/7.38 inference(quant_inst,[status(thm)],[])).
% 7.22/7.38 tff(317,plain,
% 7.22/7.38 ((~![T_b: $i, V_x: $i, V_z: $i, V_y: $i] : (c_lessequals(c_Orderings_Omax(V_x, V_y, T_b), V_z, T_b) | (~c_lessequals(V_x, V_z, T_b)) | (~c_lessequals(V_y, V_z, T_b)) | (~class_Orderings_Olinorder(T_b)))) | c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x), v_g(v_x), t_b), c_0, t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~class_Orderings_Olinorder(t_b)) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b))),
% 7.22/7.38 inference(modus_ponens,[status(thm)],[316, 315])).
% 7.22/7.38 tff(318,plain,
% 7.22/7.38 ((~class_Orderings_Olinorder(t_b)) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) | (~c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b))),
% 7.22/7.38 inference(unit_resolution,[status(thm)],[317, 311, 308])).
% 7.22/7.38 tff(319,plain,
% 7.22/7.38 (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.22/7.38 inference(unit_resolution,[status(thm)],[318, 298, 231])).
% 7.22/7.38 tff(320,plain,
% 7.22/7.38 (((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | ((~class_Orderings_Olinorder(t_b)) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | (~class_Orderings_Olinorder(t_b)) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b))),
% 7.22/7.38 inference(rewrite,[status(thm)],[])).
% 7.22/7.38 tff(321,plain,
% 7.22/7.38 ((c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~class_Orderings_Olinorder(t_b))) <=> ((~class_Orderings_Olinorder(t_b)) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b))),
% 7.22/7.38 inference(rewrite,[status(thm)],[])).
% 7.22/7.38 tff(322,plain,
% 7.22/7.38 (((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | (c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~class_Orderings_Olinorder(t_b)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | ((~class_Orderings_Olinorder(t_b)) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)))),
% 7.22/7.38 inference(monotonicity,[status(thm)],[321])).
% 7.22/7.38 tff(323,plain,
% 7.22/7.38 (((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | (c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~class_Orderings_Olinorder(t_b)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | (~class_Orderings_Olinorder(t_b)) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b))),
% 7.22/7.38 inference(transitivity,[status(thm)],[322, 320])).
% 7.22/7.38 tff(324,plain,
% 7.22/7.38 ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | (c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~class_Orderings_Olinorder(t_b)))),
% 7.22/7.38 inference(quant_inst,[status(thm)],[])).
% 7.22/7.38 tff(325,plain,
% 7.22/7.38 ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | c_less(V_y, V_x, T_a) | (~class_Orderings_Olinorder(T_a)))) | (~class_Orderings_Olinorder(t_b)) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)),
% 7.22/7.38 inference(modus_ponens,[status(thm)],[324, 323])).
% 7.22/7.38 tff(326,plain,
% 7.22/7.38 (c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)),
% 7.22/7.38 inference(unit_resolution,[status(thm)],[325, 241, 231, 319])).
% 7.22/7.38 tff(327,plain,
% 7.22/7.38 (((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | ((~class_Orderings_Oorder(t_b)) | c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | (~class_Orderings_Oorder(t_b)) | c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)))),
% 7.22/7.38 inference(rewrite,[status(thm)],[])).
% 7.22/7.38 tff(328,plain,
% 7.22/7.38 ((c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b))) <=> ((~class_Orderings_Oorder(t_b)) | c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)))),
% 7.22/7.38 inference(rewrite,[status(thm)],[])).
% 7.22/7.38 tff(329,plain,
% 7.22/7.38 (((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | ((~class_Orderings_Oorder(t_b)) | c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b))))),
% 7.22/7.38 inference(monotonicity,[status(thm)],[328])).
% 7.22/7.38 tff(330,plain,
% 7.22/7.38 (((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | (~class_Orderings_Oorder(t_b)) | c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)))),
% 7.22/7.38 inference(transitivity,[status(thm)],[329, 327])).
% 7.22/7.38 tff(331,plain,
% 7.22/7.38 ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b)))),
% 7.22/7.38 inference(quant_inst,[status(thm)],[])).
% 7.22/7.38 tff(332,plain,
% 7.22/7.38 ((~![V_x: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_y, T_a) | (~c_less(V_x, V_y, T_a)) | (~class_Orderings_Oorder(T_a)))) | (~class_Orderings_Oorder(t_b)) | c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b) | (~c_less(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b))),
% 7.22/7.38 inference(modus_ponens,[status(thm)],[331, 330])).
% 7.22/7.38 tff(333,plain,
% 7.22/7.38 (c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)),
% 7.22/7.38 inference(unit_resolution,[status(thm)],[332, 210, 200, 326])).
% 7.22/7.38 tff(334,plain,
% 7.22/7.38 (^[V_x: $i, V_z: $i, T_a: $i, V_y: $i] : refl((c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a))) <=> (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a))))),
% 7.22/7.38 inference(bind,[status(th)],[])).
% 7.22/7.38 tff(335,plain,
% 7.22/7.38 (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a))) <=> ![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.22/7.38 inference(quant_intro,[status(thm)],[334])).
% 7.22/7.38 tff(336,plain,
% 7.22/7.38 (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a))) <=> ![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.22/7.38 inference(rewrite,[status(thm)],[])).
% 7.22/7.38 tff(337,plain,
% 7.22/7.38 (^[V_x: $i, V_z: $i, T_a: $i, V_y: $i] : trans(monotonicity(rewrite((((~class_Orderings_Oorder(T_a)) | (~c_lessequals(V_y, V_z, T_a))) | (~c_lessequals(V_x, V_y, T_a))) <=> ((~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))), (((((~class_Orderings_Oorder(T_a)) | (~c_lessequals(V_y, V_z, T_a))) | (~c_lessequals(V_x, V_y, T_a))) | c_lessequals(V_x, V_z, T_a)) <=> (((~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a))) | c_lessequals(V_x, V_z, T_a)))), rewrite((((~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a))) | c_lessequals(V_x, V_z, T_a)) <=> (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))), (((((~class_Orderings_Oorder(T_a)) | (~c_lessequals(V_y, V_z, T_a))) | (~c_lessequals(V_x, V_y, T_a))) | c_lessequals(V_x, V_z, T_a)) <=> (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))))),
% 7.22/7.38 inference(bind,[status(th)],[])).
% 7.22/7.38 tff(338,plain,
% 7.22/7.38 (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((((~class_Orderings_Oorder(T_a)) | (~c_lessequals(V_y, V_z, T_a))) | (~c_lessequals(V_x, V_y, T_a))) | c_lessequals(V_x, V_z, T_a)) <=> ![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.22/7.39 inference(quant_intro,[status(thm)],[337])).
% 7.22/7.39 tff(339,axiom,(![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((((~class_Orderings_Oorder(T_a)) | (~c_lessequals(V_y, V_z, T_a))) | (~c_lessequals(V_x, V_y, T_a))) | c_lessequals(V_x, V_z, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Orderings_Oorder__class_Oorder__trans_0')).
% 7.22/7.39 tff(340,plain,
% 7.22/7.39 (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.22/7.39 inference(modus_ponens,[status(thm)],[339, 338])).
% 7.22/7.39 tff(341,plain,
% 7.22/7.39 (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.22/7.39 inference(modus_ponens,[status(thm)],[340, 336])).
% 7.22/7.39 tff(342,plain,(
% 7.22/7.39 ![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.22/7.39 inference(skolemize,[status(sab)],[341])).
% 7.22/7.39 tff(343,plain,
% 7.22/7.39 (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))),
% 7.22/7.39 inference(modus_ponens,[status(thm)],[342, 335])).
% 7.22/7.39 tff(344,plain,
% 7.22/7.39 (((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | ((~class_Orderings_Oorder(t_b)) | (~c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))) <=> ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | (~class_Orderings_Oorder(t_b)) | (~c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.22/7.39 inference(rewrite,[status(thm)],[])).
% 7.22/7.39 tff(345,plain,
% 7.22/7.39 ((c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b))) <=> ((~class_Orderings_Oorder(t_b)) | (~c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.22/7.39 inference(rewrite,[status(thm)],[])).
% 7.22/7.39 tff(346,plain,
% 7.22/7.39 (((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b)))) <=> ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | ((~class_Orderings_Oorder(t_b)) | (~c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))))),
% 7.22/7.39 inference(monotonicity,[status(thm)],[345])).
% 7.22/7.39 tff(347,plain,
% 7.22/7.39 (((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b)))) <=> ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | (~class_Orderings_Oorder(t_b)) | (~c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.22/7.39 inference(transitivity,[status(thm)],[346, 344])).
% 7.22/7.39 tff(348,plain,
% 7.22/7.39 ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b)))),
% 7.22/7.39 inference(quant_inst,[status(thm)],[])).
% 7.22/7.39 tff(349,plain,
% 7.22/7.39 ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | (~class_Orderings_Oorder(t_b)) | (~c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b)) | c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 7.22/7.39 inference(modus_ponens,[status(thm)],[348, 347])).
% 7.22/7.39 tff(350,plain,
% 7.22/7.39 (c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 7.22/7.39 inference(unit_resolution,[status(thm)],[349, 343, 200, 333])).
% 7.22/7.39 tff(351,plain,
% 7.22/7.39 (~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.22/7.39 inference(unit_resolution,[status(thm)],[350, 286])).
% 7.22/7.39 tff(352,plain,
% 7.22/7.39 (^[V_c: $i, V_b: $i, V_a: $i, T_a: $i] : refl((c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a))) <=> (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a))))),
% 7.22/7.39 inference(bind,[status(th)],[])).
% 7.22/7.39 tff(353,plain,
% 7.22/7.39 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a))) <=> ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.22/7.39 inference(quant_intro,[status(thm)],[352])).
% 7.22/7.39 tff(354,plain,
% 7.22/7.39 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a))) <=> ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.22/7.39 inference(rewrite,[status(thm)],[])).
% 7.22/7.39 tff(355,plain,
% 7.22/7.39 (^[V_c: $i, V_b: $i, V_a: $i, T_a: $i] : rewrite((((~class_OrderedGroup_Opordered__ab__group__add(T_a)) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a))) | c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a)) <=> (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a))))),
% 7.22/7.39 inference(bind,[status(th)],[])).
% 7.22/7.39 tff(356,plain,
% 7.22/7.39 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (((~class_OrderedGroup_Opordered__ab__group__add(T_a)) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a))) | c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a)) <=> ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.22/7.39 inference(quant_intro,[status(thm)],[355])).
% 7.22/7.39 tff(357,axiom,(![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (((~class_OrderedGroup_Opordered__ab__group__add(T_a)) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a))) | c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OrderedGroup_Ocompare__rls__8_1')).
% 7.22/7.39 tff(358,plain,
% 7.22/7.39 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.22/7.39 inference(modus_ponens,[status(thm)],[357, 356])).
% 7.22/7.39 tff(359,plain,
% 7.22/7.39 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.22/7.39 inference(modus_ponens,[status(thm)],[358, 354])).
% 7.22/7.39 tff(360,plain,(
% 7.22/7.39 ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.22/7.39 inference(skolemize,[status(sab)],[359])).
% 7.22/7.39 tff(361,plain,
% 7.22/7.39 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))),
% 7.22/7.39 inference(modus_ponens,[status(thm)],[360, 353])).
% 7.22/7.39 tff(362,plain,
% 7.22/7.39 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | ((~class_OrderedGroup_Opordered__ab__group__add(t_b)) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.22/7.39 inference(rewrite,[status(thm)],[])).
% 7.22/7.39 tff(363,plain,
% 7.22/7.39 ((c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b))) <=> ((~class_OrderedGroup_Opordered__ab__group__add(t_b)) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.22/7.39 inference(rewrite,[status(thm)],[])).
% 7.22/7.39 tff(364,plain,
% 7.22/7.39 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | ((~class_OrderedGroup_Opordered__ab__group__add(t_b)) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b))))),
% 7.22/7.39 inference(monotonicity,[status(thm)],[363])).
% 7.22/7.39 tff(365,plain,
% 7.22/7.39 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.22/7.39 inference(transitivity,[status(thm)],[364, 362])).
% 7.22/7.39 tff(366,plain,
% 7.22/7.39 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)))),
% 7.22/7.39 inference(quant_inst,[status(thm)],[])).
% 7.22/7.39 tff(367,plain,
% 7.22/7.39 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 7.22/7.39 inference(modus_ponens,[status(thm)],[366, 365])).
% 7.22/7.39 tff(368,plain,
% 7.22/7.39 (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.22/7.39 inference(unit_resolution,[status(thm)],[367, 361, 154, 351])).
% 7.22/7.39 tff(369,plain,
% 7.22/7.39 (((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | ((~class_Orderings_Oorder(t_b)) | c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))) <=> ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | (~class_Orderings_Oorder(t_b)) | c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.22/7.39 inference(rewrite,[status(thm)],[])).
% 7.22/7.39 tff(370,plain,
% 7.22/7.39 ((c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b))) <=> ((~class_Orderings_Oorder(t_b)) | c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.22/7.39 inference(rewrite,[status(thm)],[])).
% 7.22/7.39 tff(371,plain,
% 7.22/7.39 (((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b)))) <=> ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | ((~class_Orderings_Oorder(t_b)) | c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b))))),
% 7.22/7.39 inference(monotonicity,[status(thm)],[370])).
% 7.22/7.39 tff(372,plain,
% 7.22/7.39 (((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b)))) <=> ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | (~class_Orderings_Oorder(t_b)) | c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.22/7.39 inference(transitivity,[status(thm)],[371, 369])).
% 7.22/7.39 tff(373,plain,
% 7.22/7.39 ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b)))),
% 7.22/7.39 inference(quant_inst,[status(thm)],[])).
% 7.22/7.39 tff(374,plain,
% 7.22/7.39 ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | (~class_Orderings_Oorder(t_b)) | c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 7.22/7.39 inference(modus_ponens,[status(thm)],[373, 372])).
% 7.22/7.39 tff(375,plain,
% 7.22/7.39 ((~c_lessequals(v_k(v_x), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 7.22/7.39 inference(unit_resolution,[status(thm)],[374, 343, 200, 368])).
% 7.22/7.39 tff(376,plain,
% 7.22/7.39 ($false),
% 7.22/7.39 inference(unit_resolution,[status(thm)],[375, 249, 133])).
% 7.22/7.39 tff(377,plain,(c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b)), inference(lemma,lemma(discharge,[]))).
% 7.22/7.39 tff(378,plain,
% 7.22/7.39 (((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (c_HOL_Oabs(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b)))) <=> ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (c_HOL_Oabs(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b)))),
% 7.22/7.39 inference(rewrite,[status(thm)],[])).
% 7.22/7.39 tff(379,plain,
% 7.22/7.39 ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (c_HOL_Oabs(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b)))),
% 7.22/7.39 inference(quant_inst,[status(thm)],[])).
% 7.22/7.39 tff(380,plain,
% 7.22/7.39 ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (c_HOL_Oabs(V_a, T_a) = c_uminus(V_a, T_a)) | (~c_lessequals(V_a, c_0, T_a)))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (c_HOL_Oabs(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b))),
% 7.22/7.39 inference(modus_ponens,[status(thm)],[379, 378])).
% 7.22/7.39 tff(381,plain,
% 7.22/7.39 ((c_HOL_Oabs(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b)) | (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b))),
% 7.22/7.39 inference(unit_resolution,[status(thm)],[380, 275, 57])).
% 7.22/7.39 tff(382,plain,
% 7.22/7.39 (c_HOL_Oabs(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 7.22/7.39 inference(unit_resolution,[status(thm)],[381, 377])).
% 7.22/7.39 tff(383,plain,
% 7.22/7.39 (c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_HOL_Oabs(c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 7.22/7.39 inference(symmetry,[status(thm)],[382])).
% 7.22/7.39 tff(384,plain,
% 7.22/7.39 (c_minus(v_f(v_x), v_g(v_x), t_b) = c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.22/7.39 inference(transitivity,[status(thm)],[41, 383, 69, 43])).
% 7.22/7.39 tff(385,plain,
% 7.22/7.39 (c_plus(v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_plus(v_g(v_x), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.22/7.39 inference(monotonicity,[status(thm)],[384])).
% 7.22/7.39 tff(386,plain,
% 7.22/7.39 (c_plus(v_g(v_x), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_plus(v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.22/7.39 inference(symmetry,[status(thm)],[385])).
% 7.22/7.39 tff(387,plain,
% 7.22/7.39 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_g(v_x), c_uminus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_plus(v_g(v_x), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_g(v_x), c_uminus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_plus(v_g(v_x), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))),
% 7.22/7.40 inference(rewrite,[status(thm)],[])).
% 7.22/7.40 tff(388,plain,
% 7.22/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_g(v_x), c_uminus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_plus(v_g(v_x), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))),
% 7.22/7.40 inference(quant_inst,[status(thm)],[])).
% 7.22/7.40 tff(389,plain,
% 7.22/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_g(v_x), c_uminus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_plus(v_g(v_x), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b))),
% 7.22/7.40 inference(modus_ponens,[status(thm)],[388, 387])).
% 7.22/7.40 tff(390,plain,
% 7.22/7.40 (c_minus(v_g(v_x), c_uminus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_plus(v_g(v_x), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.22/7.40 inference(unit_resolution,[status(thm)],[389, 101, 17])).
% 7.22/7.40 tff(391,plain,
% 7.22/7.40 (c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(v_f(v_x), v_g(v_x), t_b)),
% 7.22/7.40 inference(transitivity,[status(thm)],[42, 68, 382, 40])).
% 7.22/7.40 tff(392,plain,
% 7.22/7.40 (c_uminus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.22/7.40 inference(monotonicity,[status(thm)],[391])).
% 7.22/7.40 tff(393,plain,
% 7.22/7.40 (c_uminus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_minus(v_g(v_x), v_f(v_x), t_b)),
% 7.22/7.40 inference(transitivity,[status(thm)],[392, 256])).
% 7.22/7.40 tff(394,plain,
% 7.22/7.40 (c_minus(v_g(v_x), c_uminus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(v_g(v_x), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 7.22/7.40 inference(monotonicity,[status(thm)],[393])).
% 7.22/7.40 tff(395,plain,
% 7.22/7.40 (c_minus(v_g(v_x), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(v_g(v_x), c_uminus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b)),
% 7.22/7.40 inference(symmetry,[status(thm)],[394])).
% 7.22/7.40 tff(396,assumption,(c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_g(v_x), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b)), introduced(assumption)).
% 7.22/7.40 tff(397,plain,
% 7.22/7.40 (((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_g(v_x), v_g(v_x), t_b) = c_0))) <=> ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_g(v_x), v_g(v_x), t_b) = c_0))),
% 7.22/7.40 inference(rewrite,[status(thm)],[])).
% 7.22/7.40 tff(398,plain,
% 7.22/7.40 ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_g(v_x), v_g(v_x), t_b) = c_0))),
% 7.22/7.40 inference(quant_inst,[status(thm)],[])).
% 7.22/7.40 tff(399,plain,
% 7.22/7.40 ((~![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_g(v_x), v_g(v_x), t_b) = c_0)),
% 7.22/7.40 inference(modus_ponens,[status(thm)],[398, 397])).
% 7.22/7.40 tff(400,plain,
% 7.22/7.40 (c_minus(v_g(v_x), v_g(v_x), t_b) = c_0),
% 7.22/7.40 inference(unit_resolution,[status(thm)],[399, 112, 17])).
% 7.22/7.40 tff(401,plain,
% 7.22/7.40 (c_0 = c_minus(v_g(v_x), v_g(v_x), t_b)),
% 7.22/7.40 inference(symmetry,[status(thm)],[400])).
% 7.22/7.40 tff(402,plain,
% 7.22/7.40 (c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b) = c_minus(v_g(v_x), v_g(v_x), t_b)),
% 7.22/7.40 inference(transitivity,[status(thm)],[250, 116, 401])).
% 7.22/7.40 tff(403,plain,
% 7.22/7.40 (c_plus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_g(v_x), t_b), t_b)),
% 7.22/7.40 inference(monotonicity,[status(thm)],[402])).
% 7.22/7.40 tff(404,plain,
% 7.22/7.40 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.22/7.40 inference(rewrite,[status(thm)],[])).
% 7.22/7.40 tff(405,plain,
% 7.22/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.22/7.40 inference(quant_inst,[status(thm)],[])).
% 7.22/7.40 tff(406,plain,
% 7.22/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 7.22/7.40 inference(modus_ponens,[status(thm)],[405, 404])).
% 7.22/7.40 tff(407,plain,
% 7.22/7.40 (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.22/7.40 inference(unit_resolution,[status(thm)],[406, 101, 17])).
% 7.22/7.40 tff(408,plain,
% 7.22/7.40 (c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b)),
% 7.22/7.40 inference(monotonicity,[status(thm)],[250])).
% 7.22/7.40 tff(409,plain,
% 7.22/7.40 (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.22/7.40 inference(symmetry,[status(thm)],[408])).
% 7.22/7.40 tff(410,plain,
% 7.22/7.40 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)))),
% 7.22/7.40 inference(rewrite,[status(thm)],[])).
% 7.22/7.40 tff(411,plain,
% 7.22/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)))),
% 7.22/7.40 inference(quant_inst,[status(thm)],[])).
% 7.22/7.40 tff(412,plain,
% 7.22/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b))),
% 7.22/7.40 inference(modus_ponens,[status(thm)],[411, 410])).
% 7.22/7.40 tff(413,plain,
% 7.22/7.40 (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)),
% 7.22/7.40 inference(unit_resolution,[status(thm)],[412, 35, 17])).
% 7.22/7.40 tff(414,plain,
% 7.22/7.40 (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b)),
% 7.22/7.40 inference(symmetry,[status(thm)],[413])).
% 7.22/7.40 tff(415,plain,
% 7.22/7.40 (c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b) = c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.22/7.40 inference(transitivity,[status(thm)],[250, 414, 409])).
% 7.22/7.40 tff(416,plain,
% 7.22/7.40 (c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 7.22/7.40 inference(monotonicity,[status(thm)],[415])).
% 7.22/7.40 tff(417,plain,
% 7.22/7.40 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.22/7.40 inference(rewrite,[status(thm)],[])).
% 7.22/7.40 tff(418,plain,
% 7.22/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.22/7.40 inference(quant_inst,[status(thm)],[])).
% 7.22/7.40 tff(419,plain,
% 7.22/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 7.22/7.40 inference(modus_ponens,[status(thm)],[418, 417])).
% 7.22/7.40 tff(420,plain,
% 7.22/7.40 (c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.22/7.40 inference(unit_resolution,[status(thm)],[419, 35, 17])).
% 7.22/7.40 tff(421,plain,
% 7.22/7.40 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b)))),
% 7.24/7.40 inference(rewrite,[status(thm)],[])).
% 7.24/7.40 tff(422,plain,
% 7.24/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b)))),
% 7.24/7.40 inference(quant_inst,[status(thm)],[])).
% 7.24/7.40 tff(423,plain,
% 7.24/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b))),
% 7.24/7.40 inference(modus_ponens,[status(thm)],[422, 421])).
% 7.24/7.40 tff(424,plain,
% 7.24/7.40 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b)),
% 7.24/7.40 inference(unit_resolution,[status(thm)],[423, 101, 17])).
% 7.24/7.40 tff(425,plain,
% 7.24/7.40 (c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)),
% 7.24/7.40 inference(symmetry,[status(thm)],[424])).
% 7.24/7.40 tff(426,plain,
% 7.24/7.40 (v_g(v_x) = c_plus(c_0, v_g(v_x), t_b)),
% 7.24/7.40 inference(symmetry,[status(thm)],[137])).
% 7.24/7.40 tff(427,plain,
% 7.24/7.40 (v_g(v_x) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)),
% 7.24/7.40 inference(transitivity,[status(thm)],[426, 138, 425])).
% 7.24/7.40 tff(428,plain,
% 7.24/7.40 (c_uminus(v_g(v_x), t_b) = c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b)),
% 7.24/7.40 inference(monotonicity,[status(thm)],[427])).
% 7.24/7.40 tff(429,plain,
% 7.24/7.40 (c_uminus(v_g(v_x), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b)),
% 7.24/7.40 inference(transitivity,[status(thm)],[428, 420, 416, 407, 403, 396])).
% 7.24/7.40 tff(430,plain,
% 7.24/7.40 (c_uminus(c_uminus(v_g(v_x), t_b), t_b) = c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.24/7.40 inference(monotonicity,[status(thm)],[429])).
% 7.24/7.40 tff(431,plain,
% 7.24/7.40 (c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_uminus(c_uminus(v_g(v_x), t_b), t_b)),
% 7.24/7.40 inference(symmetry,[status(thm)],[430])).
% 7.24/7.40 tff(432,plain,
% 7.24/7.40 (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.24/7.40 inference(symmetry,[status(thm)],[416])).
% 7.24/7.40 tff(433,plain,
% 7.24/7.40 (c_plus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 7.24/7.40 inference(symmetry,[status(thm)],[407])).
% 7.24/7.40 tff(434,plain,
% 7.24/7.40 (c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_g(v_x), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.24/7.40 inference(symmetry,[status(thm)],[403])).
% 7.24/7.40 tff(435,plain,
% 7.24/7.40 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_g(v_x), t_b), t_b)),
% 7.24/7.40 inference(symmetry,[status(thm)],[396])).
% 7.24/7.40 tff(436,plain,
% 7.24/7.40 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.24/7.40 inference(transitivity,[status(thm)],[435, 434, 433, 432])).
% 7.24/7.40 tff(437,plain,
% 7.24/7.40 (c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 7.24/7.40 inference(monotonicity,[status(thm)],[436])).
% 7.24/7.40 tff(438,plain,
% 7.24/7.40 (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.24/7.40 inference(symmetry,[status(thm)],[437])).
% 7.24/7.40 tff(439,plain,
% 7.24/7.40 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)))),
% 7.24/7.40 inference(rewrite,[status(thm)],[])).
% 7.24/7.40 tff(440,plain,
% 7.24/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)))),
% 7.24/7.40 inference(quant_inst,[status(thm)],[])).
% 7.24/7.40 tff(441,plain,
% 7.24/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b))),
% 7.24/7.40 inference(modus_ponens,[status(thm)],[440, 439])).
% 7.24/7.40 tff(442,plain,
% 7.24/7.40 (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)),
% 7.24/7.40 inference(unit_resolution,[status(thm)],[441, 35, 17])).
% 7.24/7.40 tff(443,plain,
% 7.24/7.40 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 7.24/7.40 inference(symmetry,[status(thm)],[442])).
% 7.24/7.40 tff(444,plain,
% 7.24/7.40 (v_g(v_x) = c_uminus(c_uminus(v_g(v_x), t_b), t_b)),
% 7.24/7.40 inference(transitivity,[status(thm)],[426, 138, 425, 443, 438, 431])).
% 7.24/7.40 tff(445,plain,
% 7.24/7.40 (c_minus(v_g(v_x), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(c_uminus(c_uminus(v_g(v_x), t_b), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 7.24/7.40 inference(monotonicity,[status(thm)],[444])).
% 7.24/7.40 tff(446,plain,
% 7.24/7.40 (c_minus(c_uminus(c_uminus(v_g(v_x), t_b), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(v_g(v_x), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 7.24/7.40 inference(symmetry,[status(thm)],[445])).
% 7.24/7.40 tff(447,plain,
% 7.24/7.40 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_uminus(c_uminus(v_g(v_x), t_b), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_uminus(c_uminus(v_g(v_x), t_b), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 7.24/7.40 inference(rewrite,[status(thm)],[])).
% 7.24/7.40 tff(448,plain,
% 7.24/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_uminus(c_uminus(v_g(v_x), t_b), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 7.24/7.40 inference(quant_inst,[status(thm)],[])).
% 7.24/7.40 tff(449,plain,
% 7.24/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_uminus(c_uminus(v_g(v_x), t_b), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b))),
% 7.24/7.40 inference(modus_ponens,[status(thm)],[448, 447])).
% 7.24/7.40 tff(450,plain,
% 7.24/7.40 (c_uminus(c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_uminus(c_uminus(v_g(v_x), t_b), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 7.24/7.40 inference(unit_resolution,[status(thm)],[449, 35, 17])).
% 7.24/7.40 tff(451,plain,
% 7.24/7.40 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))),
% 7.24/7.40 inference(rewrite,[status(thm)],[])).
% 7.24/7.40 tff(452,plain,
% 7.24/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))),
% 7.24/7.40 inference(quant_inst,[status(thm)],[])).
% 7.24/7.40 tff(453,plain,
% 7.24/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b))),
% 7.24/7.40 inference(modus_ponens,[status(thm)],[452, 451])).
% 7.24/7.40 tff(454,plain,
% 7.24/7.40 (c_uminus(c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.24/7.40 inference(unit_resolution,[status(thm)],[453, 35, 17])).
% 7.24/7.40 tff(455,plain,
% 7.24/7.40 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b)))),
% 7.24/7.40 inference(rewrite,[status(thm)],[])).
% 7.24/7.40 tff(456,plain,
% 7.24/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b)))),
% 7.24/7.40 inference(quant_inst,[status(thm)],[])).
% 7.24/7.40 tff(457,plain,
% 7.24/7.40 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b))),
% 7.24/7.40 inference(modus_ponens,[status(thm)],[456, 455])).
% 7.24/7.40 tff(458,plain,
% 7.24/7.40 (c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b)),
% 7.24/7.40 inference(unit_resolution,[status(thm)],[457, 101, 17])).
% 7.24/7.40 tff(459,plain,
% 7.24/7.40 (c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b) = c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b)),
% 7.24/7.40 inference(symmetry,[status(thm)],[458])).
% 7.24/7.40 tff(460,plain,
% 7.24/7.40 (c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b) = c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b)),
% 7.24/7.40 inference(monotonicity,[status(thm)],[384])).
% 7.24/7.40 tff(461,plain,
% 7.24/7.40 (^[V_c: $i, V_b: $i, V_a: $i, T_a: $i] : refl(((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a))) <=> ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a))))),
% 7.24/7.40 inference(bind,[status(th)],[])).
% 7.24/7.40 tff(462,plain,
% 7.24/7.40 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a))) <=> ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))),
% 7.24/7.40 inference(quant_intro,[status(thm)],[461])).
% 7.24/7.40 tff(463,plain,
% 7.24/7.40 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a))) <=> ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))),
% 7.24/7.40 inference(rewrite,[status(thm)],[])).
% 7.24/7.40 tff(464,axiom,(![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OrderedGroup_Ocompare__rls__3_0')).
% 7.24/7.40 tff(465,plain,
% 7.24/7.40 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))),
% 7.24/7.40 inference(modus_ponens,[status(thm)],[464, 463])).
% 7.24/7.40 tff(466,plain,(
% 7.24/7.40 ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))),
% 7.24/7.40 inference(skolemize,[status(sab)],[465])).
% 7.24/7.40 tff(467,plain,
% 7.24/7.40 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))),
% 7.24/7.40 inference(modus_ponens,[status(thm)],[466, 462])).
% 7.24/7.40 tff(468,plain,
% 7.24/7.40 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b) = c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b) = c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b)))),
% 7.24/7.41 inference(rewrite,[status(thm)],[])).
% 7.24/7.41 tff(469,plain,
% 7.24/7.41 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b) = c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b)))),
% 7.24/7.41 inference(quant_inst,[status(thm)],[])).
% 7.24/7.41 tff(470,plain,
% 7.24/7.41 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b) = c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b))),
% 7.24/7.41 inference(modus_ponens,[status(thm)],[469, 468])).
% 7.24/7.41 tff(471,plain,
% 7.24/7.41 (c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b) = c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b)),
% 7.24/7.41 inference(unit_resolution,[status(thm)],[470, 467, 17])).
% 7.24/7.41 tff(472,plain,
% 7.24/7.41 (c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b) = c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b)),
% 7.24/7.41 inference(symmetry,[status(thm)],[471])).
% 7.24/7.41 tff(473,plain,
% 7.24/7.41 (c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b) = c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b)),
% 7.24/7.41 inference(transitivity,[status(thm)],[472, 460, 459])).
% 7.24/7.41 tff(474,plain,
% 7.24/7.41 (c_uminus(c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_uminus(c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b)),
% 7.24/7.41 inference(monotonicity,[status(thm)],[473])).
% 7.24/7.41 tff(475,plain,
% 7.24/7.41 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), c_plus(v_f(v_x), v_g(v_x), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), c_plus(v_f(v_x), v_g(v_x), t_b), t_b)))),
% 7.24/7.41 inference(rewrite,[status(thm)],[])).
% 7.24/7.41 tff(476,plain,
% 7.24/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), c_plus(v_f(v_x), v_g(v_x), t_b), t_b)))),
% 7.24/7.41 inference(quant_inst,[status(thm)],[])).
% 7.24/7.41 tff(477,plain,
% 7.24/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), c_plus(v_f(v_x), v_g(v_x), t_b), t_b))),
% 7.24/7.41 inference(modus_ponens,[status(thm)],[476, 475])).
% 7.24/7.41 tff(478,plain,
% 7.24/7.41 (c_uminus(c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), c_plus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.24/7.41 inference(unit_resolution,[status(thm)],[477, 35, 17])).
% 7.24/7.41 tff(479,plain,
% 7.24/7.41 (c_minus(v_g(v_x), c_plus(v_f(v_x), v_g(v_x), t_b), t_b) = c_uminus(c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.24/7.41 inference(symmetry,[status(thm)],[478])).
% 7.24/7.41 tff(480,plain,
% 7.24/7.41 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b) = c_plus(v_f(v_x), v_g(v_x), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b) = c_plus(v_f(v_x), v_g(v_x), t_b)))),
% 7.24/7.41 inference(rewrite,[status(thm)],[])).
% 7.24/7.41 tff(481,plain,
% 7.24/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b) = c_plus(v_f(v_x), v_g(v_x), t_b)))),
% 7.24/7.41 inference(quant_inst,[status(thm)],[])).
% 7.24/7.41 tff(482,plain,
% 7.24/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b) = c_plus(v_f(v_x), v_g(v_x), t_b))),
% 7.24/7.41 inference(modus_ponens,[status(thm)],[481, 480])).
% 7.24/7.41 tff(483,plain,
% 7.24/7.41 (c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b) = c_plus(v_f(v_x), v_g(v_x), t_b)),
% 7.24/7.41 inference(unit_resolution,[status(thm)],[482, 101, 17])).
% 7.24/7.41 tff(484,plain,
% 7.24/7.41 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b)))),
% 7.24/7.41 inference(rewrite,[status(thm)],[])).
% 7.24/7.41 tff(485,plain,
% 7.24/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b)))),
% 7.24/7.41 inference(quant_inst,[status(thm)],[])).
% 7.24/7.41 tff(486,plain,
% 7.24/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b))),
% 7.24/7.41 inference(modus_ponens,[status(thm)],[485, 484])).
% 7.24/7.41 tff(487,plain,
% 7.24/7.41 (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b)),
% 7.24/7.41 inference(unit_resolution,[status(thm)],[486, 35, 17])).
% 7.24/7.41 tff(488,plain,
% 7.24/7.41 (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_plus(v_f(v_x), v_g(v_x), t_b)),
% 7.24/7.41 inference(transitivity,[status(thm)],[487, 483])).
% 7.24/7.41 tff(489,plain,
% 7.24/7.41 (c_minus(v_g(v_x), c_uminus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b) = c_minus(v_g(v_x), c_plus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.24/7.41 inference(monotonicity,[status(thm)],[488])).
% 7.24/7.41 tff(490,plain,
% 7.24/7.41 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_g(v_x), c_uminus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b) = c_plus(v_g(v_x), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_g(v_x), c_uminus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b) = c_plus(v_g(v_x), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b)))),
% 7.24/7.41 inference(rewrite,[status(thm)],[])).
% 7.24/7.41 tff(491,plain,
% 7.24/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_g(v_x), c_uminus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b) = c_plus(v_g(v_x), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b)))),
% 7.24/7.41 inference(quant_inst,[status(thm)],[])).
% 7.24/7.41 tff(492,plain,
% 7.24/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(v_g(v_x), c_uminus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b) = c_plus(v_g(v_x), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b))),
% 7.24/7.41 inference(modus_ponens,[status(thm)],[491, 490])).
% 7.24/7.41 tff(493,plain,
% 7.24/7.41 (c_minus(v_g(v_x), c_uminus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b) = c_plus(v_g(v_x), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b)),
% 7.24/7.41 inference(unit_resolution,[status(thm)],[492, 101, 17])).
% 7.24/7.41 tff(494,plain,
% 7.24/7.41 (c_plus(v_g(v_x), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_minus(v_g(v_x), c_uminus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b)),
% 7.24/7.41 inference(symmetry,[status(thm)],[493])).
% 7.24/7.41 tff(495,plain,
% 7.24/7.41 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(v_g(v_x), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), c_uminus(v_g(v_x), t_b), t_b), v_f(v_x), t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(v_g(v_x), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), c_uminus(v_g(v_x), t_b), t_b), v_f(v_x), t_b)))),
% 7.24/7.41 inference(rewrite,[status(thm)],[])).
% 7.24/7.41 tff(496,plain,
% 7.24/7.41 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(v_g(v_x), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), c_uminus(v_g(v_x), t_b), t_b), v_f(v_x), t_b)))),
% 7.24/7.41 inference(quant_inst,[status(thm)],[])).
% 7.24/7.41 tff(497,plain,
% 7.24/7.41 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(v_g(v_x), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), c_uminus(v_g(v_x), t_b), t_b), v_f(v_x), t_b))),
% 7.24/7.41 inference(modus_ponens,[status(thm)],[496, 495])).
% 7.24/7.41 tff(498,plain,
% 7.24/7.41 (c_plus(v_g(v_x), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), c_uminus(v_g(v_x), t_b), t_b), v_f(v_x), t_b)),
% 7.24/7.41 inference(unit_resolution,[status(thm)],[497, 24, 17])).
% 7.24/7.41 tff(499,plain,
% 7.24/7.41 (c_minus(c_plus(v_g(v_x), c_uminus(v_g(v_x), t_b), t_b), v_f(v_x), t_b) = c_plus(v_g(v_x), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b)),
% 7.24/7.41 inference(symmetry,[status(thm)],[498])).
% 7.24/7.41 tff(500,plain,
% 7.24/7.41 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), c_uminus(v_g(v_x), t_b), t_b), v_f(v_x), t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), c_uminus(v_g(v_x), t_b), t_b), v_f(v_x), t_b)))),
% 7.24/7.41 inference(rewrite,[status(thm)],[])).
% 7.24/7.41 tff(501,plain,
% 7.24/7.41 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), c_uminus(v_g(v_x), t_b), t_b), v_f(v_x), t_b)))),
% 7.24/7.41 inference(quant_inst,[status(thm)],[])).
% 7.24/7.41 tff(502,plain,
% 7.24/7.41 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), c_uminus(v_g(v_x), t_b), t_b), v_f(v_x), t_b))),
% 7.24/7.41 inference(modus_ponens,[status(thm)],[501, 500])).
% 7.24/7.41 tff(503,plain,
% 7.24/7.41 (c_plus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_minus(c_plus(v_g(v_x), c_uminus(v_g(v_x), t_b), t_b), v_f(v_x), t_b)),
% 7.24/7.41 inference(unit_resolution,[status(thm)],[502, 467, 17])).
% 7.24/7.41 tff(504,plain,
% 7.24/7.41 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b) = c_plus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b) = c_plus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)))),
% 7.24/7.41 inference(rewrite,[status(thm)],[])).
% 7.24/7.41 tff(505,plain,
% 7.24/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b) = c_plus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)))),
% 7.24/7.41 inference(quant_inst,[status(thm)],[])).
% 7.24/7.41 tff(506,plain,
% 7.24/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b) = c_plus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b))),
% 7.24/7.41 inference(modus_ponens,[status(thm)],[505, 504])).
% 7.24/7.41 tff(507,plain,
% 7.24/7.41 (c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b) = c_plus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)),
% 7.24/7.41 inference(unit_resolution,[status(thm)],[506, 101, 17])).
% 7.24/7.41 tff(508,plain,
% 7.24/7.41 (c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.24/7.41 inference(transitivity,[status(thm)],[507, 503, 499, 494, 489, 479, 474, 454])).
% 7.24/7.41 tff(509,plain,
% 7.24/7.41 (c_uminus(c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b), t_b) = c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b)),
% 7.24/7.41 inference(monotonicity,[status(thm)],[508])).
% 7.24/7.41 tff(510,plain,
% 7.24/7.41 (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_uminus(c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b), t_b)),
% 7.24/7.41 inference(symmetry,[status(thm)],[509])).
% 7.24/7.41 tff(511,plain,
% 7.24/7.41 (c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.24/7.41 inference(transitivity,[status(thm)],[383, 69, 43])).
% 7.24/7.41 tff(512,plain,
% 7.24/7.41 (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.24/7.41 inference(monotonicity,[status(thm)],[511])).
% 7.24/7.41 tff(513,plain,
% 7.24/7.41 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 7.24/7.41 inference(rewrite,[status(thm)],[])).
% 7.24/7.41 tff(514,plain,
% 7.24/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 7.24/7.41 inference(quant_inst,[status(thm)],[])).
% 7.24/7.41 tff(515,plain,
% 7.24/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b))),
% 7.24/7.41 inference(modus_ponens,[status(thm)],[514, 513])).
% 7.24/7.41 tff(516,plain,
% 7.24/7.41 (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 7.24/7.41 inference(unit_resolution,[status(thm)],[515, 101, 17])).
% 7.24/7.41 tff(517,plain,
% 7.24/7.41 (c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b)),
% 7.24/7.41 inference(symmetry,[status(thm)],[516])).
% 7.24/7.41 tff(518,plain,
% 7.24/7.41 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b)))),
% 7.24/7.41 inference(rewrite,[status(thm)],[])).
% 7.24/7.41 tff(519,plain,
% 7.24/7.41 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b)))),
% 7.24/7.41 inference(quant_inst,[status(thm)],[])).
% 7.25/7.41 tff(520,plain,
% 7.25/7.41 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b))),
% 7.25/7.41 inference(modus_ponens,[status(thm)],[519, 518])).
% 7.25/7.41 tff(521,plain,
% 7.25/7.41 (c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b)),
% 7.25/7.41 inference(unit_resolution,[status(thm)],[520, 24, 17])).
% 7.25/7.41 tff(522,plain,
% 7.25/7.41 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 7.25/7.41 inference(symmetry,[status(thm)],[521])).
% 7.25/7.41 tff(523,plain,
% 7.25/7.41 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), v_g(v_x), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), v_g(v_x), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b)))),
% 7.25/7.41 inference(rewrite,[status(thm)],[])).
% 7.25/7.41 tff(524,plain,
% 7.25/7.41 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), v_g(v_x), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b)))),
% 7.25/7.41 inference(quant_inst,[status(thm)],[])).
% 7.25/7.41 tff(525,plain,
% 7.25/7.41 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), v_g(v_x), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b))),
% 7.25/7.41 inference(modus_ponens,[status(thm)],[524, 523])).
% 7.25/7.41 tff(526,plain,
% 7.25/7.41 (c_plus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), v_g(v_x), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b)),
% 7.25/7.41 inference(unit_resolution,[status(thm)],[525, 467, 17])).
% 7.25/7.41 tff(527,plain,
% 7.25/7.41 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), v_g(v_x), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), v_g(v_x), t_b)))),
% 7.25/7.41 inference(rewrite,[status(thm)],[])).
% 7.25/7.41 tff(528,plain,
% 7.25/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), v_g(v_x), t_b)))),
% 7.25/7.41 inference(quant_inst,[status(thm)],[])).
% 7.25/7.41 tff(529,plain,
% 7.25/7.41 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), v_g(v_x), t_b))),
% 7.25/7.42 inference(modus_ponens,[status(thm)],[528, 527])).
% 7.25/7.42 tff(530,plain,
% 7.25/7.42 (c_minus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_plus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), v_g(v_x), t_b)),
% 7.25/7.42 inference(unit_resolution,[status(thm)],[529, 101, 17])).
% 7.25/7.42 tff(531,plain,
% 7.25/7.42 (c_minus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.25/7.42 inference(transitivity,[status(thm)],[530, 526, 522, 517, 512])).
% 7.25/7.42 tff(532,plain,
% 7.25/7.42 (c_uminus(c_minus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b)),
% 7.25/7.42 inference(monotonicity,[status(thm)],[531])).
% 7.25/7.42 tff(533,plain,
% 7.25/7.42 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b)))),
% 7.25/7.42 inference(rewrite,[status(thm)],[])).
% 7.25/7.42 tff(534,plain,
% 7.25/7.42 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b)))),
% 7.25/7.42 inference(quant_inst,[status(thm)],[])).
% 7.25/7.42 tff(535,plain,
% 7.25/7.42 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b))),
% 7.25/7.42 inference(modus_ponens,[status(thm)],[534, 533])).
% 7.25/7.42 tff(536,plain,
% 7.25/7.42 (c_uminus(c_minus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b)),
% 7.25/7.42 inference(unit_resolution,[status(thm)],[535, 35, 17])).
% 7.25/7.42 tff(537,plain,
% 7.25/7.42 (c_minus(c_uminus(v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_uminus(c_minus(c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b)),
% 7.25/7.42 inference(symmetry,[status(thm)],[536])).
% 7.25/7.42 tff(538,plain,
% 7.25/7.42 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b)))),
% 7.25/7.42 inference(rewrite,[status(thm)],[])).
% 7.25/7.42 tff(539,plain,
% 7.25/7.42 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b)))),
% 7.25/7.42 inference(quant_inst,[status(thm)],[])).
% 7.25/7.42 tff(540,plain,
% 7.25/7.42 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b))),
% 7.25/7.42 inference(modus_ponens,[status(thm)],[539, 538])).
% 7.25/7.42 tff(541,plain,
% 7.25/7.42 (c_uminus(c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b)),
% 7.25/7.42 inference(unit_resolution,[status(thm)],[540, 35, 17])).
% 7.25/7.42 tff(542,plain,
% 7.25/7.42 (c_plus(v_f(v_x), v_g(v_x), t_b) = c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b)),
% 7.25/7.42 inference(symmetry,[status(thm)],[483])).
% 7.25/7.42 tff(543,plain,
% 7.25/7.42 (((~![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))) | ((~class_OrderedGroup_Ocomm__monoid__add(t_b)) | (c_plus(c_0, c_plus(v_f(v_x), v_g(v_x), t_b), t_b) = c_plus(v_f(v_x), v_g(v_x), t_b)))) <=> ((~![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))) | (~class_OrderedGroup_Ocomm__monoid__add(t_b)) | (c_plus(c_0, c_plus(v_f(v_x), v_g(v_x), t_b), t_b) = c_plus(v_f(v_x), v_g(v_x), t_b)))),
% 7.25/7.42 inference(rewrite,[status(thm)],[])).
% 7.25/7.42 tff(544,plain,
% 7.25/7.42 ((~![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))) | ((~class_OrderedGroup_Ocomm__monoid__add(t_b)) | (c_plus(c_0, c_plus(v_f(v_x), v_g(v_x), t_b), t_b) = c_plus(v_f(v_x), v_g(v_x), t_b)))),
% 7.25/7.42 inference(quant_inst,[status(thm)],[])).
% 7.25/7.42 tff(545,plain,
% 7.25/7.42 ((~![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))) | (~class_OrderedGroup_Ocomm__monoid__add(t_b)) | (c_plus(c_0, c_plus(v_f(v_x), v_g(v_x), t_b), t_b) = c_plus(v_f(v_x), v_g(v_x), t_b))),
% 7.25/7.42 inference(modus_ponens,[status(thm)],[544, 543])).
% 7.25/7.42 tff(546,plain,
% 7.25/7.42 (c_plus(c_0, c_plus(v_f(v_x), v_g(v_x), t_b), t_b) = c_plus(v_f(v_x), v_g(v_x), t_b)),
% 7.25/7.42 inference(unit_resolution,[status(thm)],[545, 90, 83])).
% 7.25/7.42 tff(547,plain,
% 7.25/7.42 (c_plus(c_0, c_plus(v_f(v_x), v_g(v_x), t_b), t_b) = c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_plus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.25/7.42 inference(monotonicity,[status(thm)],[118])).
% 7.25/7.42 tff(548,plain,
% 7.25/7.42 (c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_plus(v_f(v_x), v_g(v_x), t_b), t_b) = c_plus(c_0, c_plus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.25/7.42 inference(symmetry,[status(thm)],[547])).
% 7.25/7.42 tff(549,plain,
% 7.25/7.42 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_plus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_plus(v_f(v_x), v_g(v_x), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_plus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_plus(v_f(v_x), v_g(v_x), t_b), t_b)))),
% 7.25/7.42 inference(rewrite,[status(thm)],[])).
% 7.25/7.42 tff(550,plain,
% 7.25/7.42 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_plus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_plus(v_f(v_x), v_g(v_x), t_b), t_b)))),
% 7.25/7.42 inference(quant_inst,[status(thm)],[])).
% 7.25/7.42 tff(551,plain,
% 7.25/7.42 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_plus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_plus(v_f(v_x), v_g(v_x), t_b), t_b))),
% 7.25/7.42 inference(modus_ponens,[status(thm)],[550, 549])).
% 7.25/7.42 tff(552,plain,
% 7.25/7.42 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_plus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_plus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.25/7.42 inference(unit_resolution,[status(thm)],[551, 101, 17])).
% 7.25/7.42 tff(553,plain,
% 7.25/7.42 (c_uminus(c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_uminus(c_plus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.25/7.42 inference(monotonicity,[status(thm)],[483])).
% 7.25/7.42 tff(554,plain,
% 7.25/7.42 (c_uminus(c_plus(v_f(v_x), v_g(v_x), t_b), t_b) = c_uminus(c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b), t_b)),
% 7.25/7.42 inference(symmetry,[status(thm)],[553])).
% 7.25/7.42 tff(555,plain,
% 7.25/7.42 (c_uminus(c_plus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b)),
% 7.25/7.42 inference(transitivity,[status(thm)],[554, 541])).
% 7.25/7.42 tff(556,plain,
% 7.25/7.42 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_plus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b)),
% 7.25/7.42 inference(monotonicity,[status(thm)],[555])).
% 7.25/7.42 tff(557,plain,
% 7.25/7.42 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_plus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.25/7.42 inference(symmetry,[status(thm)],[556])).
% 7.25/7.42 tff(558,plain,
% 7.25/7.42 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b) = c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b)),
% 7.25/7.42 inference(transitivity,[status(thm)],[557, 552, 548, 546, 542])).
% 7.25/7.42 tff(559,plain,
% 7.25/7.42 (c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b) = c_uminus(c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b), t_b)),
% 7.25/7.42 inference(monotonicity,[status(thm)],[558])).
% 7.25/7.42 tff(560,plain,
% 7.25/7.42 (c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b)),
% 7.25/7.42 inference(transitivity,[status(thm)],[559, 541])).
% 7.25/7.42 tff(561,plain,
% 7.25/7.42 (c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b) = c_uminus(v_g(v_x), t_b)),
% 7.25/7.42 inference(symmetry,[status(thm)],[428])).
% 7.25/7.42 tff(562,plain,
% 7.25/7.42 (c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b)),
% 7.25/7.42 inference(symmetry,[status(thm)],[420])).
% 7.25/7.42 tff(563,plain,
% 7.25/7.42 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b) = c_uminus(v_g(v_x), t_b)),
% 7.25/7.42 inference(transitivity,[status(thm)],[435, 434, 433, 432, 562, 561])).
% 7.25/7.42 tff(564,plain,
% 7.25/7.42 (c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b)),
% 7.25/7.42 inference(monotonicity,[status(thm)],[563, 560])).
% 7.25/7.42 tff(565,plain,
% 7.25/7.42 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b), t_b) = c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b), t_b) = c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b)))),
% 7.25/7.42 inference(rewrite,[status(thm)],[])).
% 7.25/7.42 tff(566,plain,
% 7.25/7.42 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b), t_b) = c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b)))),
% 7.25/7.42 inference(quant_inst,[status(thm)],[])).
% 7.25/7.42 tff(567,plain,
% 7.25/7.42 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, c_uminus(V_b, T_a), T_a) = c_plus(V_a, V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b), t_b) = c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b))),
% 7.25/7.42 inference(modus_ponens,[status(thm)],[566, 565])).
% 7.25/7.42 tff(568,plain,
% 7.25/7.42 (c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b), t_b) = c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b)),
% 7.25/7.42 inference(unit_resolution,[status(thm)],[567, 101, 17])).
% 7.25/7.42 tff(569,plain,
% 7.25/7.42 (c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b) = c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b), t_b)),
% 7.25/7.42 inference(symmetry,[status(thm)],[568])).
% 7.25/7.42 tff(570,plain,
% 7.25/7.42 (c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_plus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_uminus(c_plus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.25/7.42 inference(symmetry,[status(thm)],[552])).
% 7.25/7.42 tff(571,plain,
% 7.25/7.42 (c_plus(v_f(v_x), v_g(v_x), t_b) = c_plus(c_0, c_plus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.25/7.42 inference(symmetry,[status(thm)],[546])).
% 7.25/7.42 tff(572,plain,
% 7.25/7.42 (c_plus(v_f(v_x), v_g(v_x), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b)),
% 7.25/7.42 inference(transitivity,[status(thm)],[571, 547, 570, 556])).
% 7.25/7.42 tff(573,plain,
% 7.25/7.42 (c_plus(c_uminus(v_g(v_x), t_b), c_plus(v_f(v_x), v_g(v_x), t_b), t_b) = c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_uminus(v_g(v_x), t_b), v_f(v_x), t_b), t_b), t_b)),
% 7.25/7.42 inference(monotonicity,[status(thm)],[429, 572])).
% 7.25/7.42 tff(574,plain,
% 7.25/7.42 (c_minus(v_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(v_f(v_x), c_uminus(v_g(v_x), t_b), t_b)),
% 7.25/7.42 inference(monotonicity,[status(thm)],[563])).
% 7.25/7.42 tff(575,plain,
% 7.25/7.42 (c_minus(v_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_plus(v_f(v_x), v_g(v_x), t_b)),
% 7.25/7.42 inference(transitivity,[status(thm)],[574, 483])).
% 7.25/7.42 tff(576,plain,
% 7.25/7.42 (c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(c_uminus(v_g(v_x), t_b), c_plus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.25/7.42 inference(monotonicity,[status(thm)],[563, 575])).
% 7.25/7.42 tff(577,plain,
% 7.25/7.42 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_minus(c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_minus(c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.25/7.42 inference(rewrite,[status(thm)],[])).
% 7.25/7.42 tff(578,plain,
% 7.25/7.42 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_minus(c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.25/7.42 inference(quant_inst,[status(thm)],[])).
% 7.25/7.42 tff(579,plain,
% 7.25/7.42 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_minus(c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 7.25/7.42 inference(modus_ponens,[status(thm)],[578, 577])).
% 7.25/7.42 tff(580,plain,
% 7.25/7.42 (c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_minus(c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.25/7.42 inference(unit_resolution,[status(thm)],[579, 24, 17])).
% 7.25/7.42 tff(581,plain,
% 7.25/7.42 (c_minus(c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 7.25/7.43 inference(symmetry,[status(thm)],[580])).
% 7.25/7.43 tff(582,plain,
% 7.25/7.43 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), v_f(v_x), t_b) = c_minus(c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), v_f(v_x), t_b) = c_minus(c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.25/7.43 inference(rewrite,[status(thm)],[])).
% 7.25/7.43 tff(583,plain,
% 7.25/7.43 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), v_f(v_x), t_b) = c_minus(c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 7.25/7.43 inference(quant_inst,[status(thm)],[])).
% 7.25/7.43 tff(584,plain,
% 7.25/7.43 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(c_minus(V_a, V_b, T_a), V_c, T_a) = c_minus(c_plus(V_a, V_c, T_a), V_b, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), v_f(v_x), t_b) = c_minus(c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 7.25/7.43 inference(modus_ponens,[status(thm)],[583, 582])).
% 7.25/7.43 tff(585,plain,
% 7.25/7.43 (c_plus(c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), v_f(v_x), t_b) = c_minus(c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(unit_resolution,[status(thm)],[584, 467, 17])).
% 7.25/7.43 tff(586,plain,
% 7.25/7.43 (c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(monotonicity,[status(thm)],[563, 563])).
% 7.25/7.43 tff(587,plain,
% 7.25/7.43 (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(symmetry,[status(thm)],[586])).
% 7.25/7.43 tff(588,plain,
% 7.25/7.43 (c_minus(v_g(v_x), v_g(v_x), t_b) = c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(transitivity,[status(thm)],[400, 117, 587])).
% 7.25/7.43 tff(589,plain,
% 7.25/7.43 (c_plus(c_minus(v_g(v_x), v_g(v_x), t_b), v_f(v_x), t_b) = c_plus(c_minus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), v_f(v_x), t_b)),
% 7.25/7.43 inference(monotonicity,[status(thm)],[588])).
% 7.25/7.43 tff(590,plain,
% 7.25/7.43 (c_plus(c_minus(v_g(v_x), v_g(v_x), t_b), v_f(v_x), t_b) = c_minus(c_plus(v_g(v_x), v_f(v_x), t_b), v_g(v_x), t_b)),
% 7.25/7.43 inference(transitivity,[status(thm)],[589, 585, 581, 576, 573, 569, 564, 537, 532, 510, 450, 446, 395, 390, 386, 28])).
% 7.25/7.43 tff(591,plain,
% 7.25/7.43 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b)))),
% 7.25/7.43 inference(rewrite,[status(thm)],[])).
% 7.25/7.43 tff(592,plain,
% 7.25/7.43 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b)))),
% 7.25/7.43 inference(quant_inst,[status(thm)],[])).
% 7.25/7.43 tff(593,plain,
% 7.25/7.43 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_uminus(c_minus(V_a, V_b, T_a), T_a) = c_minus(V_b, V_a, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b))),
% 7.25/7.43 inference(modus_ponens,[status(thm)],[592, 591])).
% 7.25/7.43 tff(594,plain,
% 7.25/7.43 (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(unit_resolution,[status(thm)],[593, 35, 17])).
% 7.25/7.43 tff(595,plain,
% 7.25/7.43 (c_HOL_Oabs(c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b) = c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(monotonicity,[status(thm)],[40])).
% 7.25/7.43 tff(596,plain,
% 7.25/7.43 (c_minus(v_f(v_x), v_g(v_x), t_b) = c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(transitivity,[status(thm)],[41, 383, 69, 595])).
% 7.25/7.43 tff(597,plain,
% 7.25/7.43 (c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b) = c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b)),
% 7.25/7.43 inference(monotonicity,[status(thm)],[596])).
% 7.25/7.43 tff(598,plain,
% 7.25/7.43 (c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b) = c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(transitivity,[status(thm)],[472, 597, 459])).
% 7.25/7.43 tff(599,plain,
% 7.25/7.43 (c_uminus(c_minus(c_plus(v_f(v_x), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_uminus(c_minus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_uminus(v_g(v_x), t_b), t_b), t_b)),
% 7.25/7.43 inference(monotonicity,[status(thm)],[598])).
% 7.25/7.43 tff(600,plain,
% 7.25/7.43 (c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.25/7.43 inference(transitivity,[status(thm)],[507, 503, 499, 494, 489, 479, 599, 454])).
% 7.25/7.43 tff(601,plain,
% 7.25/7.43 (c_uminus(c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b), t_b) = c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b)),
% 7.25/7.43 inference(monotonicity,[status(thm)],[600])).
% 7.25/7.43 tff(602,plain,
% 7.25/7.43 (c_minus(c_uminus(c_uminus(v_g(v_x), t_b), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_uminus(c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_uminus(c_uminus(v_g(v_x), t_b), t_b), t_b), t_b)),
% 7.25/7.43 inference(symmetry,[status(thm)],[450])).
% 7.25/7.43 tff(603,plain,
% 7.25/7.43 (c_uminus(v_g(v_x), t_b) = c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(transitivity,[status(thm)],[428, 420])).
% 7.25/7.43 tff(604,plain,
% 7.25/7.43 (c_uminus(c_uminus(v_g(v_x), t_b), t_b) = c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 7.25/7.43 inference(monotonicity,[status(thm)],[603])).
% 7.25/7.43 tff(605,plain,
% 7.25/7.43 (c_uminus(c_minus(c_uminus(v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_uminus(c_uminus(v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(symmetry,[status(thm)],[604])).
% 7.25/7.43 tff(606,plain,
% 7.25/7.43 (v_g(v_x) = c_uminus(c_uminus(v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(transitivity,[status(thm)],[426, 138, 425, 443, 605])).
% 7.25/7.43 tff(607,plain,
% 7.25/7.43 (c_minus(v_g(v_x), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) = c_minus(c_uminus(c_uminus(v_g(v_x), t_b), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 7.25/7.43 inference(monotonicity,[status(thm)],[606])).
% 7.25/7.43 tff(608,plain,
% 7.25/7.43 (c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_HOL_Oabs(c_uminus(c_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b)),
% 7.25/7.43 inference(symmetry,[status(thm)],[595])).
% 7.25/7.43 tff(609,plain,
% 7.25/7.43 (c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(v_f(v_x), v_g(v_x), t_b)),
% 7.25/7.43 inference(transitivity,[status(thm)],[608, 68, 382, 40])).
% 7.25/7.43 tff(610,plain,
% 7.25/7.43 (c_uminus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_uminus(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(monotonicity,[status(thm)],[609])).
% 7.25/7.43 tff(611,plain,
% 7.25/7.43 (c_uminus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_minus(v_g(v_x), v_f(v_x), t_b)),
% 7.25/7.43 inference(transitivity,[status(thm)],[610, 256])).
% 7.25/7.43 tff(612,plain,
% 7.25/7.43 (c_minus(v_g(v_x), c_uminus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(v_g(v_x), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 7.25/7.43 inference(monotonicity,[status(thm)],[611])).
% 7.25/7.43 tff(613,plain,
% 7.25/7.43 (c_plus(v_g(v_x), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_minus(v_g(v_x), c_uminus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b)),
% 7.25/7.43 inference(symmetry,[status(thm)],[390])).
% 7.25/7.43 tff(614,plain,
% 7.25/7.43 (c_plus(v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_plus(v_g(v_x), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 7.25/7.43 inference(monotonicity,[status(thm)],[596])).
% 7.25/7.43 tff(615,plain,
% 7.25/7.43 (c_minus(c_plus(v_g(v_x), v_f(v_x), t_b), v_g(v_x), t_b) = c_plus(v_g(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(symmetry,[status(thm)],[28])).
% 7.25/7.43 tff(616,assumption,(c_plus(c_minus(v_g(v_x), v_g(v_x), t_b), v_f(v_x), t_b) = c_minus(c_plus(v_g(v_x), v_f(v_x), t_b), v_g(v_x), t_b)), introduced(assumption)).
% 7.25/7.43 tff(617,plain,
% 7.25/7.43 (c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b) = c_plus(c_minus(v_g(v_x), v_g(v_x), t_b), v_f(v_x), t_b)),
% 7.25/7.43 inference(monotonicity,[status(thm)],[402])).
% 7.25/7.43 tff(618,plain,
% 7.25/7.43 (v_f(v_x) = c_plus(c_0, v_f(v_x), t_b)),
% 7.25/7.43 inference(symmetry,[status(thm)],[94])).
% 7.25/7.43 tff(619,plain,
% 7.25/7.43 (v_f(v_x) = c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b)),
% 7.25/7.43 inference(transitivity,[status(thm)],[618, 119, 617, 616, 615, 614, 613, 612, 607, 602, 601, 594, 458])).
% 7.25/7.43 tff(620,plain,
% 7.25/7.43 (c_lessequals(v_k(v_x), v_f(v_x), t_b) <=> c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b)),
% 7.25/7.43 inference(monotonicity,[status(thm)],[619])).
% 7.25/7.43 tff(621,plain,
% 7.25/7.43 (c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b) <=> c_lessequals(v_k(v_x), v_f(v_x), t_b)),
% 7.25/7.43 inference(symmetry,[status(thm)],[620])).
% 7.25/7.43 tff(622,plain,
% 7.25/7.43 ((~c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b)) <=> (~c_lessequals(v_k(v_x), v_f(v_x), t_b))),
% 7.25/7.43 inference(monotonicity,[status(thm)],[621])).
% 7.25/7.43 tff(623,plain,
% 7.25/7.43 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b)))),
% 7.25/7.43 inference(rewrite,[status(thm)],[])).
% 7.25/7.43 tff(624,plain,
% 7.25/7.43 ((c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b))) <=> (c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b)))),
% 7.25/7.43 inference(rewrite,[status(thm)],[])).
% 7.25/7.43 tff(625,plain,
% 7.25/7.43 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b))))),
% 7.25/7.43 inference(monotonicity,[status(thm)],[624])).
% 7.25/7.43 tff(626,plain,
% 7.25/7.43 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b)))),
% 7.25/7.43 inference(transitivity,[status(thm)],[625, 623])).
% 7.25/7.43 tff(627,plain,
% 7.25/7.43 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | (c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)))),
% 7.25/7.44 inference(quant_inst,[status(thm)],[])).
% 7.25/7.44 tff(628,plain,
% 7.25/7.44 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(c_minus(V_a, V_b, T_a), V_c, T_a) | (~c_lessequals(V_a, c_plus(V_c, V_b, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__group__add(T_a)))) | c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b))),
% 7.25/7.44 inference(modus_ponens,[status(thm)],[627, 626])).
% 7.25/7.44 tff(629,plain,
% 7.25/7.44 ((~class_OrderedGroup_Opordered__ab__group__add(t_b)) | (~c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b))),
% 7.25/7.44 inference(unit_resolution,[status(thm)],[628, 361, 319])).
% 7.25/7.44 tff(630,plain,
% 7.25/7.44 (~c_lessequals(v_k(v_x), c_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b), t_b)),
% 7.25/7.44 inference(unit_resolution,[status(thm)],[629, 154])).
% 7.25/7.44 tff(631,plain,
% 7.25/7.44 (~c_lessequals(v_k(v_x), v_f(v_x), t_b)),
% 7.25/7.44 inference(modus_ponens,[status(thm)],[630, 622])).
% 7.25/7.44 tff(632,plain,
% 7.25/7.44 ($false),
% 7.25/7.44 inference(unit_resolution,[status(thm)],[132, 631])).
% 7.25/7.44 tff(633,plain,(~(c_plus(c_minus(v_g(v_x), v_g(v_x), t_b), v_f(v_x), t_b) = c_minus(c_plus(v_g(v_x), v_f(v_x), t_b), v_g(v_x), t_b))), inference(lemma,lemma(discharge,[]))).
% 7.25/7.44 tff(634,plain,
% 7.25/7.44 ($false),
% 7.25/7.44 inference(unit_resolution,[status(thm)],[633, 590])).
% 7.25/7.44 tff(635,plain,(~(c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_g(v_x), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b))), inference(lemma,lemma(discharge,[]))).
% 7.25/7.44 tff(636,plain,
% 7.25/7.44 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_g(v_x), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_g(v_x), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b)))),
% 7.25/7.44 inference(rewrite,[status(thm)],[])).
% 7.25/7.44 tff(637,plain,
% 7.25/7.44 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | ((~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_g(v_x), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b)))),
% 7.25/7.44 inference(quant_inst,[status(thm)],[])).
% 7.25/7.44 tff(638,plain,
% 7.25/7.44 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_plus(V_a, c_minus(V_b, V_c, T_a), T_a) = c_minus(c_plus(V_a, V_b, T_a), V_c, T_a)))) | (~class_OrderedGroup_Oab__group__add(t_b)) | (c_plus(c_uminus(v_g(v_x), t_b), c_minus(v_g(v_x), v_g(v_x), t_b), t_b) = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b))),
% 7.25/7.44 inference(modus_ponens,[status(thm)],[637, 636])).
% 7.25/7.44 tff(639,plain,
% 7.25/7.44 ($false),
% 7.25/7.44 inference(unit_resolution,[status(thm)],[638, 24, 17, 635])).
% 7.25/7.44 % SZS output end Proof
% 7.25/7.44 % E exiting
%------------------------------------------------------------------------------