TSTP Solution File: ANA022-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA022-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 16:23:28 EDT 2022
% Result : Unsatisfiable 0.83s 0.78s
% Output : Proof 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA022-2 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n001.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 29 19:33:45 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.83/0.78 % SZS status Unsatisfiable
% 0.83/0.78 % SZS output start Proof
% 0.83/0.78 tff(c_minus_type, type, (
% 0.83/0.78 c_minus: ( $i * $i * $i ) > $i)).
% 0.83/0.78 tff(t_b_type, type, (
% 0.83/0.78 t_b: $i)).
% 0.83/0.78 tff(c_plus_type, type, (
% 0.83/0.78 c_plus: ( $i * $i * $i ) > $i)).
% 0.83/0.78 tff(v_g_type, type, (
% 0.83/0.78 v_g: $i > $i)).
% 0.83/0.78 tff(v_x_type, type, (
% 0.83/0.78 v_x: $i)).
% 0.83/0.78 tff(c_uminus_type, type, (
% 0.83/0.78 c_uminus: ( $i * $i ) > $i)).
% 0.83/0.78 tff(v_f_type, type, (
% 0.83/0.78 v_f: $i > $i)).
% 0.83/0.78 tff(c_lessequals_type, type, (
% 0.83/0.78 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.83/0.78 tff(v_k_type, type, (
% 0.83/0.78 v_k: $i > $i)).
% 0.83/0.78 tff(c_HOL_Oabs_type, type, (
% 0.83/0.78 c_HOL_Oabs: ( $i * $i ) > $i)).
% 0.83/0.78 tff(class_OrderedGroup_Oab__group__add_type, type, (
% 0.83/0.78 class_OrderedGroup_Oab__group__add: $i > $o)).
% 0.83/0.78 tff(class_Ring__and__Field_Oordered__idom_type, type, (
% 0.83/0.78 class_Ring__and__Field_Oordered__idom: $i > $o)).
% 0.83/0.78 tff(c_0_type, type, (
% 0.83/0.78 c_0: $i)).
% 0.83/0.78 tff(class_OrderedGroup_Ocomm__monoid__add_type, type, (
% 0.83/0.78 class_OrderedGroup_Ocomm__monoid__add: $i > $o)).
% 0.83/0.78 tff(class_OrderedGroup_Olordered__ab__group__abs_type, type, (
% 0.83/0.78 class_OrderedGroup_Olordered__ab__group__abs: $i > $o)).
% 0.83/0.78 tff(c_less_type, type, (
% 0.83/0.78 c_less: ( $i * $i * $i ) > $o)).
% 0.83/0.78 tff(class_OrderedGroup_Opordered__ab__group__add_type, type, (
% 0.83/0.78 class_OrderedGroup_Opordered__ab__group__add: $i > $o)).
% 0.83/0.78 tff(class_Orderings_Olinorder_type, type, (
% 0.83/0.78 class_Orderings_Olinorder: $i > $o)).
% 0.83/0.78 tff(class_Orderings_Oorder_type, type, (
% 0.83/0.78 class_Orderings_Oorder: $i > $o)).
% 0.83/0.78 tff(class_LOrder_Ojoin__semilorder_type, type, (
% 0.83/0.78 class_LOrder_Ojoin__semilorder: $i > $o)).
% 0.83/0.78 tff(c_Orderings_Omax_type, type, (
% 0.83/0.78 c_Orderings_Omax: ( $i * $i * $i ) > $i)).
% 0.83/0.78 tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type, type, (
% 0.83/0.78 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o)).
% 0.83/0.78 tff(1,plain,
% 0.83/0.78 (^[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))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(2,plain,
% 0.83/0.78 (![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)))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[1])).
% 0.83/0.78 tff(3,plain,
% 0.83/0.78 (![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)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(4,plain,
% 0.83/0.78 (^[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))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(5,plain,
% 0.83/0.78 (![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)))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[4])).
% 0.83/0.78 tff(6,axiom,(![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Oab__group__add(T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clsrel_Ring__and__Field_Oordered__idom_4')).
% 0.83/0.78 tff(7,plain,
% 0.83/0.78 (![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.83/0.78 tff(8,plain,
% 0.83/0.78 (![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.83/0.78 tff(9,plain,(
% 0.83/0.78 ![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.78 inference(skolemize,[status(sab)],[8])).
% 0.83/0.78 tff(10,plain,
% 0.83/0.78 (![T: $i] : (class_OrderedGroup_Oab__group__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.83/0.78 tff(11,plain,
% 0.83/0.78 (class_Ring__and__Field_Oordered__idom(t_b) <=> class_Ring__and__Field_Oordered__idom(t_b)),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(12,axiom,(class_Ring__and__Field_Oordered__idom(t_b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','tfree_tcs')).
% 0.83/0.78 tff(13,plain,
% 0.83/0.78 (class_Ring__and__Field_Oordered__idom(t_b)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.83/0.78 tff(14,plain,
% 0.83/0.78 (((~![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)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(15,plain,
% 0.83/0.78 ((~![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)))),
% 0.83/0.78 inference(quant_inst,[status(thm)],[])).
% 0.83/0.78 tff(16,plain,
% 0.83/0.78 ((~![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))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.83/0.78 tff(17,plain,
% 0.83/0.78 (class_OrderedGroup_Oab__group__add(t_b)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[16, 13, 10])).
% 0.83/0.78 tff(18,plain,
% 0.83/0.78 (^[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))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(19,plain,
% 0.83/0.78 (![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)))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[18])).
% 0.83/0.78 tff(20,plain,
% 0.83/0.78 (![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)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(21,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/sandbox/benchmark/theBenchmark.p','cls_OrderedGroup_Odiff__minus__eq__add_0')).
% 0.83/0.78 tff(22,plain,
% 0.83/0.78 (![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)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.83/0.78 tff(23,plain,(
% 0.83/0.78 ![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)))),
% 0.83/0.78 inference(skolemize,[status(sab)],[22])).
% 0.83/0.78 tff(24,plain,
% 0.83/0.78 (![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)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.83/0.78 tff(25,plain,
% 0.83/0.78 (((~![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)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(26,plain,
% 0.83/0.78 ((~![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)))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(27,plain,
% 0.83/0.79 ((~![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))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.83/0.79 tff(28,plain,
% 0.83/0.79 (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)),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[27, 24, 17])).
% 0.83/0.79 tff(29,plain,
% 0.83/0.79 (((~![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)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(30,plain,
% 0.83/0.79 ((~![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)))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(31,plain,
% 0.83/0.79 ((~![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))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.83/0.79 tff(32,plain,
% 0.83/0.79 (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)),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[31, 24, 17])).
% 0.83/0.79 tff(33,plain,
% 0.83/0.79 (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)),
% 0.83/0.79 inference(symmetry,[status(thm)],[32])).
% 0.83/0.79 tff(34,plain,
% 0.83/0.79 (((~![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)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(35,plain,
% 0.83/0.79 ((~![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)))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(36,plain,
% 0.83/0.79 ((~![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))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.83/0.79 tff(37,plain,
% 0.83/0.79 (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)),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[36, 24, 17])).
% 0.83/0.79 tff(38,plain,
% 0.83/0.79 (^[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)))),
% 0.83/0.79 inference(bind,[status(th)],[])).
% 0.83/0.79 tff(39,plain,
% 0.83/0.79 (![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))),
% 0.83/0.79 inference(quant_intro,[status(thm)],[38])).
% 0.83/0.79 tff(40,plain,
% 0.83/0.79 (![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))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(41,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/sandbox/benchmark/theBenchmark.p','cls_OrderedGroup_Odiff__self_0')).
% 0.83/0.79 tff(42,plain,
% 0.83/0.79 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.83/0.79 tff(43,plain,(
% 0.83/0.79 ![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))),
% 0.83/0.79 inference(skolemize,[status(sab)],[42])).
% 0.83/0.79 tff(44,plain,
% 0.83/0.79 (![V_a: $i, T_a: $i] : ((~class_OrderedGroup_Oab__group__add(T_a)) | (c_minus(V_a, V_a, T_a) = c_0))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.83/0.79 tff(45,plain,
% 0.83/0.79 (((~![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))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(46,plain,
% 0.83/0.79 ((~![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))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(47,plain,
% 0.83/0.79 ((~![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)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.83/0.79 tff(48,plain,
% 0.83/0.79 (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b) = c_0),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[47, 44, 17])).
% 0.83/0.79 tff(49,plain,
% 0.83/0.79 (c_0 = c_minus(c_uminus(v_g(v_x), t_b), c_uminus(v_g(v_x), t_b), t_b)),
% 0.83/0.79 inference(symmetry,[status(thm)],[48])).
% 0.83/0.79 tff(50,plain,
% 0.83/0.79 (c_0 = c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b)),
% 0.83/0.79 inference(transitivity,[status(thm)],[49, 37])).
% 0.83/0.79 tff(51,plain,
% 0.83/0.79 (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)),
% 0.83/0.79 inference(monotonicity,[status(thm)],[50])).
% 0.83/0.79 tff(52,plain,
% 0.83/0.79 (^[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))))),
% 0.83/0.79 inference(bind,[status(th)],[])).
% 0.83/0.79 tff(53,plain,
% 0.83/0.79 (![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)))),
% 0.83/0.79 inference(quant_intro,[status(thm)],[52])).
% 0.83/0.79 tff(54,plain,
% 0.83/0.79 (![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)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(55,plain,
% 0.83/0.79 (^[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))))),
% 0.83/0.79 inference(bind,[status(th)],[])).
% 0.83/0.79 tff(56,plain,
% 0.83/0.79 (![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)))),
% 0.83/0.79 inference(quant_intro,[status(thm)],[55])).
% 0.83/0.79 tff(57,axiom,(![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Ocomm__monoid__add(T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clsrel_Ring__and__Field_Oordered__idom_23')).
% 0.83/0.79 tff(58,plain,
% 0.83/0.79 (![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.83/0.79 tff(59,plain,
% 0.83/0.79 (![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.83/0.79 tff(60,plain,(
% 0.83/0.79 ![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.79 inference(skolemize,[status(sab)],[59])).
% 0.83/0.79 tff(61,plain,
% 0.83/0.79 (![T: $i] : (class_OrderedGroup_Ocomm__monoid__add(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.83/0.79 tff(62,plain,
% 0.83/0.79 (((~![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)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(63,plain,
% 0.83/0.79 ((~![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)))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(64,plain,
% 0.83/0.79 ((~![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))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.83/0.79 tff(65,plain,
% 0.83/0.79 (class_OrderedGroup_Ocomm__monoid__add(t_b)),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[64, 13, 61])).
% 0.83/0.79 tff(66,plain,
% 0.83/0.79 (^[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)))),
% 0.83/0.79 inference(bind,[status(th)],[])).
% 0.83/0.79 tff(67,plain,
% 0.83/0.79 (![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))),
% 0.83/0.79 inference(quant_intro,[status(thm)],[66])).
% 0.83/0.79 tff(68,plain,
% 0.83/0.79 (![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))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(69,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/sandbox/benchmark/theBenchmark.p','cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0')).
% 0.83/0.79 tff(70,plain,
% 0.83/0.79 (![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.83/0.79 tff(71,plain,(
% 0.83/0.79 ![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))),
% 0.83/0.79 inference(skolemize,[status(sab)],[70])).
% 0.83/0.79 tff(72,plain,
% 0.83/0.79 (![T_a: $i, V_y: $i] : ((~class_OrderedGroup_Ocomm__monoid__add(T_a)) | (c_plus(c_0, V_y, T_a) = V_y))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.83/0.79 tff(73,plain,
% 0.83/0.79 (((~![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)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(74,plain,
% 0.83/0.79 ((~![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)))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(75,plain,
% 0.83/0.79 ((~![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))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.83/0.79 tff(76,plain,
% 0.83/0.79 (c_plus(c_0, v_g(v_x), t_b) = v_g(v_x)),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[75, 72, 65])).
% 0.83/0.79 tff(77,plain,
% 0.83/0.79 (v_g(v_x) = c_plus(c_0, v_g(v_x), t_b)),
% 0.83/0.79 inference(symmetry,[status(thm)],[76])).
% 0.83/0.79 tff(78,plain,
% 0.83/0.79 (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)),
% 0.83/0.79 inference(transitivity,[status(thm)],[77, 51, 33])).
% 0.83/0.79 tff(79,plain,
% 0.83/0.79 (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)),
% 0.83/0.79 inference(monotonicity,[status(thm)],[78])).
% 0.83/0.79 tff(80,plain,
% 0.83/0.79 (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)),
% 0.83/0.79 inference(symmetry,[status(thm)],[79])).
% 0.83/0.79 tff(81,plain,
% 0.83/0.79 (^[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))))),
% 0.83/0.79 inference(bind,[status(th)],[])).
% 0.83/0.79 tff(82,plain,
% 0.83/0.79 (![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)))),
% 0.83/0.79 inference(quant_intro,[status(thm)],[81])).
% 0.83/0.79 tff(83,plain,
% 0.83/0.79 (![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)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(84,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/sandbox/benchmark/theBenchmark.p','cls_OrderedGroup_Ominus__diff__eq_0')).
% 0.83/0.79 tff(85,plain,
% 0.83/0.79 (![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)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.83/0.79 tff(86,plain,(
% 0.83/0.79 ![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)))),
% 0.83/0.79 inference(skolemize,[status(sab)],[85])).
% 0.83/0.79 tff(87,plain,
% 0.83/0.79 (![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)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.83/0.79 tff(88,plain,
% 0.83/0.79 (((~![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)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(89,plain,
% 0.83/0.79 ((~![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)))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(90,plain,
% 0.83/0.79 ((~![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))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.83/0.79 tff(91,plain,
% 0.83/0.79 (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)),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[90, 87, 17])).
% 0.83/0.79 tff(92,plain,
% 0.83/0.79 (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)),
% 0.83/0.79 inference(symmetry,[status(thm)],[91])).
% 0.83/0.79 tff(93,plain,
% 0.83/0.79 (((~![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_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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), 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_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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_0))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(94,plain,
% 0.83/0.79 ((~![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_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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_0))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(95,plain,
% 0.83/0.79 ((~![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_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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_0)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.83/0.79 tff(96,plain,
% 0.83/0.79 (c_minus(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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_0),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[95, 44, 17])).
% 0.83/0.79 tff(97,plain,
% 0.83/0.79 (v_g(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)),
% 0.83/0.79 inference(transitivity,[status(thm)],[77, 51])).
% 0.83/0.79 tff(98,plain,
% 0.83/0.79 (c_minus(v_g(v_x), v_g(v_x), t_b) = c_minus(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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.79 inference(monotonicity,[status(thm)],[97, 97])).
% 0.83/0.79 tff(99,plain,
% 0.83/0.79 (c_minus(v_g(v_x), 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)),
% 0.83/0.79 inference(transitivity,[status(thm)],[98, 96, 49])).
% 0.83/0.79 tff(100,plain,
% 0.83/0.79 (c_uminus(c_minus(v_g(v_x), 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)),
% 0.83/0.79 inference(monotonicity,[status(thm)],[99])).
% 0.83/0.79 tff(101,plain,
% 0.83/0.79 (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_minus(v_g(v_x), v_g(v_x), t_b), t_b)),
% 0.83/0.79 inference(symmetry,[status(thm)],[100])).
% 0.83/0.79 tff(102,plain,
% 0.83/0.79 (((~![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)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(103,plain,
% 0.83/0.79 ((~![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)))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(104,plain,
% 0.83/0.79 ((~![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))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.83/0.79 tff(105,plain,
% 0.83/0.79 (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)),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[104, 87, 17])).
% 0.83/0.79 tff(106,plain,
% 0.83/0.79 (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)),
% 0.83/0.79 inference(symmetry,[status(thm)],[105])).
% 0.83/0.79 tff(107,plain,
% 0.83/0.79 (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)),
% 0.83/0.79 inference(symmetry,[status(thm)],[37])).
% 0.83/0.79 tff(108,plain,
% 0.83/0.79 (c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b) = c_uminus(c_minus(v_g(v_x), v_g(v_x), t_b), t_b)),
% 0.83/0.79 inference(transitivity,[status(thm)],[107, 106, 101])).
% 0.83/0.79 tff(109,plain,
% 0.83/0.79 (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_minus(v_g(v_x), v_g(v_x), t_b), t_b), t_b)),
% 0.83/0.79 inference(monotonicity,[status(thm)],[108])).
% 0.83/0.79 tff(110,plain,
% 0.83/0.79 (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_minus(v_g(v_x), 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)),
% 0.83/0.79 inference(symmetry,[status(thm)],[109])).
% 0.83/0.79 tff(111,plain,
% 0.83/0.79 (((~![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_g(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_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_minus(v_g(v_x), v_g(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_g(v_x), t_b), t_b)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(112,plain,
% 0.83/0.80 ((~![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_g(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_g(v_x), t_b), t_b)))),
% 0.83/0.80 inference(quant_inst,[status(thm)],[])).
% 0.83/0.80 tff(113,plain,
% 0.83/0.80 ((~![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_g(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_g(v_x), t_b), t_b))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.83/0.80 tff(114,plain,
% 0.83/0.80 (c_minus(c_uminus(v_g(v_x), t_b), c_uminus(c_minus(v_g(v_x), v_g(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_g(v_x), t_b), t_b)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[113, 24, 17])).
% 0.83/0.80 tff(115,plain,
% 0.83/0.80 (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_uminus(v_g(v_x), t_b), c_uminus(c_minus(v_g(v_x), v_g(v_x), t_b), t_b), t_b)),
% 0.83/0.80 inference(symmetry,[status(thm)],[114])).
% 0.83/0.80 tff(116,plain,
% 0.83/0.80 (^[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))))),
% 0.83/0.80 inference(bind,[status(th)],[])).
% 0.83/0.80 tff(117,plain,
% 0.83/0.80 (![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)))),
% 0.83/0.80 inference(quant_intro,[status(thm)],[116])).
% 0.83/0.80 tff(118,plain,
% 0.83/0.80 (![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)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(119,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/sandbox/benchmark/theBenchmark.p','cls_OrderedGroup_Ocompare__rls__2_0')).
% 0.83/0.80 tff(120,plain,
% 0.83/0.80 (![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)))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.83/0.80 tff(121,plain,(
% 0.83/0.80 ![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)))),
% 0.83/0.80 inference(skolemize,[status(sab)],[120])).
% 0.83/0.80 tff(122,plain,
% 0.83/0.80 (![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)))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.83/0.80 tff(123,plain,
% 0.83/0.80 (((~![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)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(124,plain,
% 0.83/0.80 ((~![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)))),
% 0.83/0.80 inference(quant_inst,[status(thm)],[])).
% 0.83/0.80 tff(125,plain,
% 0.83/0.80 ((~![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))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.83/0.80 tff(126,plain,
% 0.83/0.80 (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)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[125, 122, 17])).
% 0.83/0.80 tff(127,plain,
% 0.83/0.80 (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)),
% 0.83/0.80 inference(symmetry,[status(thm)],[126])).
% 0.83/0.80 tff(128,plain,
% 0.83/0.80 (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)),
% 0.83/0.80 inference(transitivity,[status(thm)],[127, 115, 110, 92, 80])).
% 0.83/0.80 tff(129,plain,
% 0.83/0.80 (((~![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)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(130,plain,
% 0.83/0.80 ((~![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)))),
% 0.83/0.80 inference(quant_inst,[status(thm)],[])).
% 0.83/0.80 tff(131,plain,
% 0.83/0.80 ((~![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))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.83/0.80 tff(132,plain,
% 0.83/0.80 ((~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))),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[131, 87])).
% 0.83/0.80 tff(133,plain,
% 0.83/0.80 (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)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[132, 17])).
% 0.83/0.80 tff(134,plain,
% 0.83/0.80 (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)),
% 0.83/0.80 inference(symmetry,[status(thm)],[133])).
% 0.83/0.80 tff(135,plain,
% 0.83/0.80 (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)),
% 0.83/0.80 inference(monotonicity,[status(thm)],[134])).
% 0.83/0.80 tff(136,plain,
% 0.83/0.80 (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)),
% 0.83/0.80 inference(symmetry,[status(thm)],[135])).
% 0.83/0.80 tff(137,plain,
% 0.83/0.80 (^[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))))),
% 0.83/0.80 inference(bind,[status(th)],[])).
% 0.83/0.80 tff(138,plain,
% 0.83/0.80 (![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)))),
% 0.83/0.80 inference(quant_intro,[status(thm)],[137])).
% 0.83/0.80 tff(139,plain,
% 0.83/0.80 (![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)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(140,plain,
% 0.83/0.80 (^[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))))),
% 0.83/0.80 inference(bind,[status(th)],[])).
% 0.83/0.80 tff(141,plain,
% 0.83/0.80 (![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)))),
% 0.83/0.80 inference(quant_intro,[status(thm)],[140])).
% 0.83/0.80 tff(142,axiom,(![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clsrel_Ring__and__Field_Oordered__idom_50')).
% 0.83/0.80 tff(143,plain,
% 0.83/0.80 (![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.83/0.80 tff(144,plain,
% 0.83/0.80 (![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.83/0.80 tff(145,plain,(
% 0.83/0.80 ![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.80 inference(skolemize,[status(sab)],[144])).
% 0.83/0.80 tff(146,plain,
% 0.83/0.80 (![T: $i] : (class_OrderedGroup_Olordered__ab__group__abs(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.83/0.80 tff(147,plain,
% 0.83/0.80 (((~![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)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(148,plain,
% 0.83/0.80 ((~![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)))),
% 0.83/0.80 inference(quant_inst,[status(thm)],[])).
% 0.83/0.80 tff(149,plain,
% 0.83/0.80 ((~![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))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.83/0.80 tff(150,plain,
% 0.83/0.80 (class_OrderedGroup_Olordered__ab__group__abs(t_b)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[149, 13, 146])).
% 0.83/0.80 tff(151,plain,
% 0.83/0.80 (^[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))))),
% 0.83/0.80 inference(bind,[status(th)],[])).
% 0.83/0.80 tff(152,plain,
% 0.83/0.80 (![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)))),
% 0.83/0.80 inference(quant_intro,[status(thm)],[151])).
% 0.83/0.80 tff(153,plain,
% 0.83/0.80 (![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)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(154,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/sandbox/benchmark/theBenchmark.p','cls_OrderedGroup_Oabs__minus__cancel_0')).
% 0.83/0.80 tff(155,plain,
% 0.83/0.80 (![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)))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.83/0.80 tff(156,plain,(
% 0.83/0.80 ![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)))),
% 0.83/0.80 inference(skolemize,[status(sab)],[155])).
% 0.83/0.80 tff(157,plain,
% 0.83/0.80 (![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)))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.83/0.80 tff(158,plain,
% 0.83/0.80 (((~![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)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(159,plain,
% 0.83/0.80 ((~![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)))),
% 0.83/0.80 inference(quant_inst,[status(thm)],[])).
% 0.83/0.80 tff(160,plain,
% 0.83/0.80 ((~![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))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.83/0.80 tff(161,plain,
% 0.83/0.80 (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)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[160, 157, 150])).
% 0.83/0.80 tff(162,plain,
% 0.83/0.80 (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)),
% 0.83/0.80 inference(symmetry,[status(thm)],[161])).
% 0.83/0.80 tff(163,plain,
% 0.83/0.80 (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)),
% 0.83/0.80 inference(symmetry,[status(thm)],[51])).
% 0.83/0.80 tff(164,plain,
% 0.83/0.80 (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)),
% 0.83/0.80 inference(transitivity,[status(thm)],[163, 76])).
% 0.83/0.80 tff(165,plain,
% 0.83/0.80 (c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), 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)),
% 0.83/0.80 inference(monotonicity,[status(thm)],[164])).
% 0.83/0.80 tff(166,plain,
% 0.83/0.80 (c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b) = v_g(v_x)),
% 0.83/0.80 inference(transitivity,[status(thm)],[165, 163, 76])).
% 0.83/0.80 tff(167,plain,
% 0.83/0.80 (c_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), v_f(v_x), t_b) = c_minus(v_g(v_x), v_f(v_x), t_b)),
% 0.83/0.80 inference(monotonicity,[status(thm)],[166])).
% 0.83/0.80 tff(168,plain,
% 0.83/0.80 (((~![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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(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_f(v_x), t_b), t_b) = c_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), 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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(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_f(v_x), t_b), t_b) = c_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), v_f(v_x), t_b)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(169,plain,
% 0.83/0.80 ((~![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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(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_f(v_x), t_b), t_b) = c_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), v_f(v_x), t_b)))),
% 0.83/0.80 inference(quant_inst,[status(thm)],[])).
% 0.83/0.80 tff(170,plain,
% 0.83/0.80 ((~![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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(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_f(v_x), t_b), t_b) = c_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), v_f(v_x), t_b))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.83/0.80 tff(171,plain,
% 0.83/0.80 (c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(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_f(v_x), t_b), t_b) = c_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), v_f(v_x), t_b)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[170, 122, 17])).
% 0.83/0.80 tff(172,plain,
% 0.83/0.80 (c_minus(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_f(v_x), t_b) = c_minus(v_g(v_x), v_f(v_x), t_b)),
% 0.83/0.80 inference(monotonicity,[status(thm)],[164])).
% 0.83/0.80 tff(173,plain,
% 0.83/0.80 (c_minus(v_g(v_x), v_f(v_x), t_b) = c_minus(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_f(v_x), t_b)),
% 0.83/0.80 inference(symmetry,[status(thm)],[172])).
% 0.83/0.80 tff(174,plain,
% 0.83/0.80 (c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(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_minus(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_f(v_x), t_b), t_b)),
% 0.83/0.80 inference(monotonicity,[status(thm)],[173])).
% 0.83/0.80 tff(175,plain,
% 0.83/0.80 (((~![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_minus(v_g(v_x), v_f(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_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_plus(c_uminus(v_g(v_x), t_b), 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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(176,plain,
% 0.83/0.80 ((~![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_minus(v_g(v_x), v_f(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_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 0.83/0.80 inference(quant_inst,[status(thm)],[])).
% 0.83/0.80 tff(177,plain,
% 0.83/0.80 ((~![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_minus(v_g(v_x), v_f(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_minus(v_g(v_x), v_f(v_x), t_b), t_b))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.83/0.80 tff(178,plain,
% 0.83/0.80 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[177, 24, 17])).
% 0.83/0.80 tff(179,plain,
% 0.83/0.80 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(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_minus(v_g(v_x), v_f(v_x), t_b), t_b), t_b)),
% 0.83/0.80 inference(monotonicity,[status(thm)],[134])).
% 0.83/0.80 tff(180,plain,
% 0.83/0.80 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), 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)),
% 0.83/0.80 inference(transitivity,[status(thm)],[179, 178, 174, 171, 167])).
% 0.83/0.80 tff(181,plain,
% 0.83/0.80 (c_lessequals(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_0, t_b) <=> c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b)),
% 0.83/0.80 inference(monotonicity,[status(thm)],[180])).
% 0.83/0.80 tff(182,assumption,(~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)), introduced(assumption)).
% 0.83/0.80 tff(183,plain,
% 0.83/0.80 (((~![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)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(184,plain,
% 0.83/0.80 ((~![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)))),
% 0.83/0.80 inference(quant_inst,[status(thm)],[])).
% 0.83/0.80 tff(185,plain,
% 0.83/0.80 ((~![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))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.83/0.81 tff(186,plain,
% 0.83/0.81 (c_plus(c_0, v_f(v_x), t_b) = v_f(v_x)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[185, 72, 65])).
% 0.83/0.81 tff(187,plain,
% 0.83/0.81 (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)),
% 0.83/0.81 inference(monotonicity,[status(thm)],[50])).
% 0.83/0.81 tff(188,plain,
% 0.83/0.81 (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)),
% 0.83/0.81 inference(symmetry,[status(thm)],[187])).
% 0.83/0.81 tff(189,plain,
% 0.83/0.81 (c_minus(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_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_uminus(v_g(v_x), t_b), v_g(v_x), t_b)),
% 0.83/0.81 inference(transitivity,[status(thm)],[96, 49, 37])).
% 0.83/0.81 tff(190,plain,
% 0.83/0.81 (c_plus(c_minus(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_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_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b)),
% 0.83/0.81 inference(monotonicity,[status(thm)],[189])).
% 0.83/0.81 tff(191,plain,
% 0.83/0.81 (^[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))))),
% 0.83/0.81 inference(bind,[status(th)],[])).
% 0.83/0.81 tff(192,plain,
% 0.83/0.81 (![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)))),
% 0.83/0.81 inference(quant_intro,[status(thm)],[191])).
% 0.83/0.81 tff(193,plain,
% 0.83/0.81 (![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)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(194,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/sandbox/benchmark/theBenchmark.p','cls_OrderedGroup_Ocompare__rls__3_0')).
% 0.83/0.81 tff(195,plain,
% 0.83/0.81 (![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)))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.83/0.81 tff(196,plain,(
% 0.83/0.81 ![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)))),
% 0.83/0.81 inference(skolemize,[status(sab)],[195])).
% 0.83/0.81 tff(197,plain,
% 0.83/0.81 (![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)))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.83/0.81 tff(198,plain,
% 0.83/0.81 (((~![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_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_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_plus(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_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] : ((~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_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_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_plus(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_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)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(199,plain,
% 0.83/0.81 ((~![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_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_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_plus(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_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)))),
% 0.83/0.81 inference(quant_inst,[status(thm)],[])).
% 0.83/0.81 tff(200,plain,
% 0.83/0.81 ((~![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_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_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_plus(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_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))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.83/0.81 tff(201,plain,
% 0.83/0.81 (c_plus(c_minus(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_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_plus(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_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)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[200, 197, 17])).
% 0.83/0.81 tff(202,plain,
% 0.83/0.81 (c_minus(c_plus(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_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_plus(c_minus(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_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)),
% 0.83/0.81 inference(symmetry,[status(thm)],[201])).
% 0.83/0.81 tff(203,plain,
% 0.83/0.81 (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)),
% 0.83/0.81 inference(transitivity,[status(thm)],[188, 186])).
% 0.83/0.81 tff(204,plain,
% 0.83/0.81 (c_minus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.81 inference(monotonicity,[status(thm)],[203])).
% 0.83/0.81 tff(205,plain,
% 0.83/0.81 (((~![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_plus(c_uminus(v_g(v_x), t_b), 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_f(v_x), t_b) = c_minus(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_uminus(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_plus(c_uminus(v_g(v_x), t_b), 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_f(v_x), t_b) = c_minus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(206,plain,
% 0.83/0.81 ((~![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_plus(c_uminus(v_g(v_x), t_b), 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_f(v_x), t_b) = c_minus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.83/0.81 inference(quant_inst,[status(thm)],[])).
% 0.83/0.81 tff(207,plain,
% 0.83/0.81 ((~![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_plus(c_uminus(v_g(v_x), t_b), 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_f(v_x), t_b) = c_minus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.83/0.81 tff(208,plain,
% 0.83/0.81 (c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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_f(v_x), t_b) = c_minus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[207, 197, 17])).
% 0.83/0.81 tff(209,plain,
% 0.83/0.81 (((~![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_plus(c_uminus(v_g(v_x), t_b), 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_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_plus(c_uminus(v_g(v_x), t_b), 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_0))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(210,plain,
% 0.83/0.81 ((~![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_plus(c_uminus(v_g(v_x), t_b), 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_0))),
% 0.83/0.81 inference(quant_inst,[status(thm)],[])).
% 0.83/0.81 tff(211,plain,
% 0.83/0.81 ((~![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_plus(c_uminus(v_g(v_x), t_b), 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_0)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.83/0.81 tff(212,plain,
% 0.83/0.81 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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_0),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[211, 44, 17])).
% 0.83/0.81 tff(213,plain,
% 0.83/0.81 (c_0 = c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.81 inference(symmetry,[status(thm)],[212])).
% 0.83/0.81 tff(214,plain,
% 0.83/0.81 (c_plus(c_uminus(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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.81 inference(transitivity,[status(thm)],[107, 48, 213])).
% 0.83/0.81 tff(215,plain,
% 0.83/0.81 (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(c_plus(c_uminus(v_g(v_x), t_b), 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_f(v_x), t_b)),
% 0.83/0.81 inference(monotonicity,[status(thm)],[214])).
% 0.83/0.81 tff(216,plain,
% 0.83/0.81 (v_f(v_x) = c_plus(c_0, v_f(v_x), t_b)),
% 0.83/0.81 inference(symmetry,[status(thm)],[186])).
% 0.83/0.81 tff(217,plain,
% 0.83/0.81 (v_f(v_x) = c_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.81 inference(transitivity,[status(thm)],[216, 187, 215, 208, 204])).
% 0.83/0.81 tff(218,plain,
% 0.83/0.81 (c_plus(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_f(v_x), t_b) = c_plus(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(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 0.83/0.81 inference(monotonicity,[status(thm)],[217])).
% 0.83/0.81 tff(219,plain,
% 0.83/0.81 (c_plus(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(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(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_f(v_x), t_b)),
% 0.83/0.81 inference(symmetry,[status(thm)],[218])).
% 0.83/0.81 tff(220,plain,
% 0.83/0.81 (c_minus(c_plus(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(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), v_g(v_x), t_b), t_b) = c_minus(c_plus(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_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)),
% 0.83/0.81 inference(monotonicity,[status(thm)],[219])).
% 0.83/0.81 tff(221,plain,
% 0.83/0.81 (((~![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_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_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), t_b) = c_minus(c_plus(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(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), 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_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_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), t_b) = c_minus(c_plus(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(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), v_g(v_x), t_b), t_b)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(222,plain,
% 0.83/0.81 ((~![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_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_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), t_b) = c_minus(c_plus(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(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), v_g(v_x), t_b), t_b)))),
% 0.83/0.81 inference(quant_inst,[status(thm)],[])).
% 0.83/0.81 tff(223,plain,
% 0.83/0.81 ((~![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_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_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), t_b) = c_minus(c_plus(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(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), v_g(v_x), t_b), t_b))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.83/0.81 tff(224,plain,
% 0.83/0.81 (c_plus(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_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), t_b) = c_minus(c_plus(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(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), v_g(v_x), t_b), t_b)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[223, 122, 17])).
% 0.83/0.81 tff(225,plain,
% 0.83/0.81 (((~![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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(v_f(v_x), 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(v_f(v_x), c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(226,plain,
% 0.83/0.81 ((~![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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.83/0.81 inference(quant_inst,[status(thm)],[])).
% 0.83/0.81 tff(227,plain,
% 0.83/0.81 ((~![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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.83/0.81 tff(228,plain,
% 0.83/0.81 (c_minus(v_f(v_x), c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[227, 24, 17])).
% 0.83/0.81 tff(229,plain,
% 0.83/0.81 (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)),
% 0.83/0.81 inference(monotonicity,[status(thm)],[107])).
% 0.83/0.81 tff(230,plain,
% 0.83/0.81 (c_uminus(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), v_g(v_x), t_b)),
% 0.83/0.81 inference(transitivity,[status(thm)],[229, 105, 37])).
% 0.83/0.81 tff(231,plain,
% 0.83/0.81 (c_minus(v_f(v_x), c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.81 inference(monotonicity,[status(thm)],[230])).
% 0.83/0.81 tff(232,plain,
% 0.83/0.81 (c_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(v_f(v_x), c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 0.83/0.81 inference(symmetry,[status(thm)],[231])).
% 0.83/0.81 tff(233,plain,
% 0.83/0.81 (c_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_plus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.81 inference(transitivity,[status(thm)],[232, 228])).
% 0.83/0.81 tff(234,plain,
% 0.83/0.81 (c_minus(c_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b) = c_minus(c_plus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b)),
% 0.83/0.81 inference(monotonicity,[status(thm)],[233])).
% 0.83/0.81 tff(235,plain,
% 0.83/0.81 (c_minus(c_plus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b) = c_minus(c_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b)),
% 0.83/0.82 inference(symmetry,[status(thm)],[234])).
% 0.83/0.82 tff(236,plain,
% 0.83/0.82 (((~![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_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), t_b) = c_minus(c_plus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), 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_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), t_b) = c_minus(c_plus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(237,plain,
% 0.83/0.82 ((~![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_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), t_b) = c_minus(c_plus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b)))),
% 0.83/0.82 inference(quant_inst,[status(thm)],[])).
% 0.83/0.82 tff(238,plain,
% 0.83/0.82 ((~![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_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), t_b) = c_minus(c_plus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.83/0.82 tff(239,plain,
% 0.83/0.82 (c_plus(v_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), t_b) = c_minus(c_plus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[238, 122, 17])).
% 0.83/0.82 tff(240,plain,
% 0.83/0.82 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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), 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)),
% 0.83/0.82 inference(monotonicity,[status(thm)],[164])).
% 0.83/0.82 tff(241,plain,
% 0.83/0.82 (c_plus(v_f(v_x), c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), t_b) = c_plus(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)),
% 0.83/0.82 inference(monotonicity,[status(thm)],[240])).
% 0.83/0.82 tff(242,plain,
% 0.83/0.82 (c_plus(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), c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), t_b)),
% 0.83/0.82 inference(symmetry,[status(thm)],[241])).
% 0.83/0.82 tff(243,plain,
% 0.83/0.82 (((~![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(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(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)))) <=> ((~![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(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(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)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(244,plain,
% 0.83/0.82 ((~![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(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(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)))),
% 0.83/0.82 inference(quant_inst,[status(thm)],[])).
% 0.83/0.82 tff(245,plain,
% 0.83/0.82 ((~![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(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(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))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.83/0.82 tff(246,plain,
% 0.83/0.82 (c_minus(v_f(v_x), 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), t_b) = c_plus(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)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[245, 24, 17])).
% 0.83/0.82 tff(247,plain,
% 0.83/0.82 (((~![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)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(248,plain,
% 0.83/0.82 ((~![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)))),
% 0.83/0.82 inference(quant_inst,[status(thm)],[])).
% 0.83/0.82 tff(249,plain,
% 0.83/0.82 ((~![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))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.83/0.82 tff(250,plain,
% 0.83/0.82 (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)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[249, 87, 17])).
% 0.83/0.82 tff(251,plain,
% 0.83/0.82 (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)),
% 0.83/0.82 inference(transitivity,[status(thm)],[127, 115, 110])).
% 0.83/0.82 tff(252,plain,
% 0.83/0.82 (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)),
% 0.83/0.82 inference(monotonicity,[status(thm)],[251])).
% 0.83/0.82 tff(253,plain,
% 0.83/0.82 (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) = v_g(v_x)),
% 0.83/0.82 inference(transitivity,[status(thm)],[252, 250, 32, 163, 76])).
% 0.83/0.82 tff(254,plain,
% 0.83/0.82 (c_minus(v_f(v_x), 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), t_b) = c_minus(v_f(v_x), v_g(v_x), t_b)),
% 0.83/0.82 inference(monotonicity,[status(thm)],[253])).
% 0.83/0.82 tff(255,plain,
% 0.83/0.82 (c_minus(v_f(v_x), v_g(v_x), t_b) = c_minus(v_f(v_x), 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), t_b)),
% 0.83/0.82 inference(symmetry,[status(thm)],[254])).
% 0.83/0.82 tff(256,plain,
% 0.83/0.82 (c_minus(v_f(v_x), v_g(v_x), t_b) = c_minus(c_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b)),
% 0.83/0.82 inference(transitivity,[status(thm)],[255, 246, 242, 239, 235])).
% 0.83/0.82 tff(257,plain,
% 0.83/0.82 (c_plus(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(v_f(v_x), v_g(v_x), t_b), t_b) = c_plus(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_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), t_b)),
% 0.83/0.82 inference(monotonicity,[status(thm)],[256])).
% 0.83/0.82 tff(258,plain,
% 0.83/0.82 (((~![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_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_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), 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_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_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), v_f(v_x), t_b)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(259,plain,
% 0.83/0.82 ((~![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_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_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), v_f(v_x), t_b)))),
% 0.83/0.82 inference(quant_inst,[status(thm)],[])).
% 0.83/0.82 tff(260,plain,
% 0.83/0.82 ((~![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_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_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), v_f(v_x), t_b))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.83/0.82 tff(261,plain,
% 0.83/0.82 (c_plus(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_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_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), v_f(v_x), t_b)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[260, 197, 17])).
% 0.83/0.82 tff(262,plain,
% 0.83/0.82 (((~![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), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), 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), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(263,plain,
% 0.83/0.82 ((~![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), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.83/0.82 inference(quant_inst,[status(thm)],[])).
% 0.83/0.82 tff(264,plain,
% 0.83/0.82 ((~![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), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.83/0.82 tff(265,plain,
% 0.83/0.82 (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_minus(v_g(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[264, 87, 17])).
% 0.83/0.82 tff(266,plain,
% 0.83/0.82 (c_minus(v_g(v_x), 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), v_g(v_x), t_b), t_b)),
% 0.83/0.82 inference(symmetry,[status(thm)],[265])).
% 0.83/0.82 tff(267,plain,
% 0.83/0.82 (c_minus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.82 inference(monotonicity,[status(thm)],[164])).
% 0.83/0.82 tff(268,plain,
% 0.83/0.82 (c_minus(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_uminus(v_g(v_x), t_b), 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)),
% 0.83/0.82 inference(transitivity,[status(thm)],[267, 266, 252, 250, 32])).
% 0.83/0.82 tff(269,plain,
% 0.83/0.82 (c_plus(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_minus(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_uminus(v_g(v_x), t_b), v_g(v_x), 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_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)),
% 0.83/0.82 inference(monotonicity,[status(thm)],[268])).
% 0.83/0.82 tff(270,plain,
% 0.83/0.82 (((~![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_f(v_x), t_b), c_minus(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_uminus(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_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_plus(c_uminus(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_f(v_x), t_b), c_minus(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_uminus(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_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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.83/0.83 inference(rewrite,[status(thm)],[])).
% 0.83/0.83 tff(271,plain,
% 0.83/0.83 ((~![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_f(v_x), t_b), c_minus(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_uminus(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_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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.83/0.83 inference(quant_inst,[status(thm)],[])).
% 0.83/0.83 tff(272,plain,
% 0.83/0.83 ((~![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_f(v_x), t_b), c_minus(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_uminus(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_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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.83/0.83 tff(273,plain,
% 0.83/0.83 (c_plus(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_minus(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_uminus(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_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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.83 inference(unit_resolution,[status(thm)],[272, 122, 17])).
% 0.83/0.83 tff(274,plain,
% 0.83/0.83 (c_minus(c_plus(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_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_uminus(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_f(v_x), t_b), c_minus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 0.83/0.83 inference(symmetry,[status(thm)],[273])).
% 0.83/0.83 tff(275,plain,
% 0.83/0.83 (c_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), v_f(v_x), t_b) = c_plus(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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.83 inference(symmetry,[status(thm)],[261])).
% 0.83/0.83 tff(276,plain,
% 0.83/0.83 (c_minus(v_g(v_x), v_f(v_x), t_b) = c_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), v_f(v_x), t_b)),
% 0.83/0.83 inference(symmetry,[status(thm)],[167])).
% 0.83/0.83 tff(277,plain,
% 0.83/0.83 (c_minus(v_g(v_x), v_f(v_x), t_b) = c_plus(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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.83 inference(transitivity,[status(thm)],[276, 275])).
% 0.83/0.83 tff(278,plain,
% 0.83/0.83 (c_minus(c_minus(v_g(v_x), v_f(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_plus(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_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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.83/0.83 inference(monotonicity,[status(thm)],[277])).
% 0.83/0.83 tff(279,plain,
% 0.83/0.83 (c_minus(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(v_g(v_x), v_f(v_x), t_b)),
% 0.83/0.83 inference(transitivity,[status(thm)],[278, 274, 269, 261, 167])).
% 0.83/0.83 tff(280,plain,
% 0.83/0.83 (c_uminus(c_minus(c_minus(v_g(v_x), v_f(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(v_g(v_x), v_f(v_x), t_b), t_b)),
% 0.83/0.83 inference(monotonicity,[status(thm)],[279])).
% 0.83/0.83 tff(281,plain,
% 0.83/0.83 (((~![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_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_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_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_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 0.83/0.83 inference(rewrite,[status(thm)],[])).
% 0.83/0.83 tff(282,plain,
% 0.83/0.83 ((~![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_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_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 0.83/0.83 inference(quant_inst,[status(thm)],[])).
% 0.83/0.83 tff(283,plain,
% 0.83/0.83 ((~![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_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_minus(v_g(v_x), v_f(v_x), t_b), t_b))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.83/0.83 tff(284,plain,
% 0.83/0.83 (c_uminus(c_minus(c_minus(v_g(v_x), v_f(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_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 0.83/0.83 inference(unit_resolution,[status(thm)],[283, 87, 17])).
% 0.83/0.83 tff(285,plain,
% 0.83/0.83 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), 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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 0.83/0.83 inference(symmetry,[status(thm)],[284])).
% 0.83/0.83 tff(286,plain,
% 0.83/0.83 (((~![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)))),
% 0.83/0.83 inference(rewrite,[status(thm)],[])).
% 0.83/0.83 tff(287,plain,
% 0.83/0.83 ((~![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)))),
% 0.83/0.83 inference(quant_inst,[status(thm)],[])).
% 0.83/0.83 tff(288,plain,
% 0.83/0.83 ((~![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))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.83/0.83 tff(289,plain,
% 0.83/0.83 ((~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))),
% 0.83/0.83 inference(unit_resolution,[status(thm)],[288, 87])).
% 0.83/0.83 tff(290,plain,
% 0.83/0.83 (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)),
% 0.83/0.83 inference(unit_resolution,[status(thm)],[289, 17])).
% 0.83/0.83 tff(291,plain,
% 0.83/0.83 (c_lessequals(v_f(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_f(v_x), v_g(v_x), t_b)),
% 0.83/0.83 inference(monotonicity,[status(thm)],[164])).
% 0.83/0.83 tff(292,plain,
% 0.83/0.83 (c_lessequals(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_f(v_x), t_b) <=> c_lessequals(v_g(v_x), v_f(v_x), t_b)),
% 0.83/0.83 inference(monotonicity,[status(thm)],[164])).
% 0.83/0.83 tff(293,plain,
% 0.83/0.83 (c_lessequals(v_g(v_x), v_f(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_g(v_x), t_b), v_f(v_x), t_b)),
% 0.83/0.83 inference(symmetry,[status(thm)],[292])).
% 0.83/0.83 tff(294,plain,
% 0.83/0.83 ((~c_lessequals(v_g(v_x), v_f(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_g(v_x), t_b), v_f(v_x), t_b))),
% 0.83/0.83 inference(monotonicity,[status(thm)],[293])).
% 0.83/0.83 tff(295,assumption,(~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b)), introduced(assumption)).
% 0.83/0.83 tff(296,plain,
% 0.83/0.83 (^[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)))),
% 0.83/0.83 inference(bind,[status(th)],[])).
% 0.83/0.83 tff(297,plain,
% 0.83/0.83 (![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))),
% 0.83/0.83 inference(quant_intro,[status(thm)],[296])).
% 0.83/0.83 tff(298,plain,
% 0.83/0.83 (![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))),
% 0.83/0.83 inference(rewrite,[status(thm)],[])).
% 0.83/0.83 tff(299,axiom,(![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clsrel_OrderedGroup_Olordered__ab__group__abs_1')).
% 0.83/0.83 tff(300,plain,
% 0.83/0.83 (![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.83/0.83 tff(301,plain,(
% 0.83/0.83 ![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))),
% 0.83/0.83 inference(skolemize,[status(sab)],[300])).
% 0.83/0.83 tff(302,plain,
% 0.83/0.83 (![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__group__add(T))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[301, 297])).
% 0.83/0.83 tff(303,plain,
% 0.83/0.83 (((~![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))),
% 0.83/0.83 inference(rewrite,[status(thm)],[])).
% 0.83/0.83 tff(304,plain,
% 0.83/0.83 ((~![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))),
% 0.83/0.83 inference(quant_inst,[status(thm)],[])).
% 0.83/0.83 tff(305,plain,
% 0.83/0.83 ((~![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)),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.83/0.83 tff(306,plain,
% 0.83/0.83 (class_OrderedGroup_Opordered__ab__group__add(t_b)),
% 0.83/0.83 inference(unit_resolution,[status(thm)],[305, 302, 150])).
% 0.83/0.83 tff(307,plain,
% 0.83/0.83 (^[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))))),
% 0.83/0.83 inference(bind,[status(th)],[])).
% 0.83/0.83 tff(308,plain,
% 0.83/0.83 (![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)))),
% 0.83/0.83 inference(quant_intro,[status(thm)],[307])).
% 0.83/0.83 tff(309,plain,
% 0.83/0.83 (![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)))),
% 0.83/0.83 inference(rewrite,[status(thm)],[])).
% 0.83/0.83 tff(310,plain,
% 0.83/0.83 (^[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))))),
% 0.83/0.83 inference(bind,[status(th)],[])).
% 0.83/0.83 tff(311,plain,
% 0.83/0.83 (![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)))),
% 0.83/0.83 inference(quant_intro,[status(thm)],[310])).
% 0.83/0.83 tff(312,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/sandbox/benchmark/theBenchmark.p','cls_OrderedGroup_Odiff__le__0__iff__le_1')).
% 0.83/0.83 tff(313,plain,
% 0.83/0.83 (![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)))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.83/0.83 tff(314,plain,
% 0.83/0.83 (![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)))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[313, 309])).
% 0.83/0.83 tff(315,plain,(
% 0.83/0.83 ![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)))),
% 0.83/0.83 inference(skolemize,[status(sab)],[314])).
% 0.83/0.83 tff(316,plain,
% 0.83/0.83 (![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)))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[315, 308])).
% 0.83/0.83 tff(317,plain,
% 0.83/0.83 (((~![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)))),
% 0.83/0.83 inference(rewrite,[status(thm)],[])).
% 0.83/0.83 tff(318,plain,
% 0.83/0.83 ((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)))),
% 0.83/0.83 inference(rewrite,[status(thm)],[])).
% 0.83/0.83 tff(319,plain,
% 0.83/0.83 (((~![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))))),
% 0.83/0.83 inference(monotonicity,[status(thm)],[318])).
% 0.83/0.83 tff(320,plain,
% 0.83/0.83 (((~![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)))),
% 0.83/0.83 inference(transitivity,[status(thm)],[319, 317])).
% 0.83/0.83 tff(321,plain,
% 0.83/0.83 ((~![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)))),
% 0.83/0.83 inference(quant_inst,[status(thm)],[])).
% 0.83/0.83 tff(322,plain,
% 0.83/0.83 ((~![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))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.83/0.83 tff(323,plain,
% 0.83/0.83 (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))),
% 0.83/0.83 inference(unit_resolution,[status(thm)],[322, 316, 306])).
% 0.83/0.83 tff(324,plain,
% 0.83/0.83 (~c_lessequals(v_g(v_x), v_f(v_x), t_b)),
% 0.83/0.83 inference(unit_resolution,[status(thm)],[323, 295])).
% 0.83/0.83 tff(325,plain,
% 0.83/0.83 (~c_lessequals(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_f(v_x), t_b)),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[324, 294])).
% 0.83/0.83 tff(326,plain,
% 0.83/0.83 (^[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)))),
% 0.83/0.83 inference(bind,[status(th)],[])).
% 0.83/0.83 tff(327,plain,
% 0.83/0.83 (![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))),
% 0.83/0.83 inference(quant_intro,[status(thm)],[326])).
% 0.83/0.83 tff(328,plain,
% 0.83/0.83 (![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))),
% 0.83/0.83 inference(rewrite,[status(thm)],[])).
% 0.83/0.83 tff(329,axiom,(![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clsrel_Ring__and__Field_Oordered__idom_33')).
% 0.83/0.83 tff(330,plain,
% 0.83/0.83 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.83/0.83 tff(331,plain,(
% 0.83/0.83 ![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))),
% 0.83/0.83 inference(skolemize,[status(sab)],[330])).
% 0.83/0.83 tff(332,plain,
% 0.83/0.83 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_Orderings_Olinorder(T))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[331, 327])).
% 0.83/0.83 tff(333,plain,
% 0.83/0.83 (((~![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)))),
% 0.83/0.83 inference(rewrite,[status(thm)],[])).
% 0.83/0.83 tff(334,plain,
% 0.83/0.83 (((~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)))),
% 0.83/0.83 inference(rewrite,[status(thm)],[])).
% 0.83/0.83 tff(335,plain,
% 0.83/0.83 (((~![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))))),
% 0.83/0.83 inference(monotonicity,[status(thm)],[334])).
% 0.83/0.83 tff(336,plain,
% 0.83/0.83 (((~![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)))),
% 0.83/0.83 inference(transitivity,[status(thm)],[335, 333])).
% 0.83/0.83 tff(337,plain,
% 0.83/0.83 ((~![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))),
% 0.83/0.83 inference(quant_inst,[status(thm)],[])).
% 0.83/0.83 tff(338,plain,
% 0.83/0.83 ((~![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))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.83/0.83 tff(339,plain,
% 0.83/0.83 (class_Orderings_Olinorder(t_b)),
% 0.83/0.83 inference(unit_resolution,[status(thm)],[338, 13, 332])).
% 0.83/0.83 tff(340,plain,
% 0.83/0.83 (^[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))))),
% 0.83/0.83 inference(bind,[status(th)],[])).
% 0.83/0.83 tff(341,plain,
% 0.83/0.83 (![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)))),
% 0.83/0.83 inference(quant_intro,[status(thm)],[340])).
% 0.83/0.83 tff(342,plain,
% 0.83/0.83 (![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)))),
% 0.83/0.83 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(343,plain,
% 0.83/0.84 (^[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))))),
% 0.83/0.84 inference(bind,[status(th)],[])).
% 0.83/0.84 tff(344,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(quant_intro,[status(thm)],[343])).
% 0.83/0.84 tff(345,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/sandbox/benchmark/theBenchmark.p','cls_Orderings_Olinorder__not__le_0')).
% 0.83/0.84 tff(346,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.83/0.84 tff(347,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[346, 342])).
% 0.83/0.84 tff(348,plain,(
% 0.83/0.84 ![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)))),
% 0.83/0.84 inference(skolemize,[status(sab)],[347])).
% 0.83/0.84 tff(349,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[348, 341])).
% 0.83/0.84 tff(350,plain,
% 0.83/0.84 (((~![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_less(v_f(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(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_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_less(v_f(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(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_f(v_x), t_b))),
% 0.83/0.84 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(351,plain,
% 0.83/0.84 ((c_lessequals(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_f(v_x), t_b) | c_less(v_f(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_Orderings_Olinorder(t_b))) <=> ((~class_Orderings_Olinorder(t_b)) | c_less(v_f(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(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_f(v_x), t_b))),
% 0.83/0.84 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(352,plain,
% 0.83/0.84 (((~![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_plus(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_less(v_f(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_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_less(v_f(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(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_f(v_x), t_b)))),
% 0.83/0.84 inference(monotonicity,[status(thm)],[351])).
% 0.83/0.84 tff(353,plain,
% 0.83/0.84 (((~![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_plus(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_less(v_f(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_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_less(v_f(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(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_f(v_x), t_b))),
% 0.83/0.84 inference(transitivity,[status(thm)],[352, 350])).
% 0.83/0.84 tff(354,plain,
% 0.83/0.84 ((~![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_plus(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_less(v_f(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_Orderings_Olinorder(t_b)))),
% 0.83/0.84 inference(quant_inst,[status(thm)],[])).
% 0.83/0.84 tff(355,plain,
% 0.83/0.84 ((~![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_less(v_f(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(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_f(v_x), t_b)),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.83/0.84 tff(356,plain,
% 0.83/0.84 (c_less(v_f(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(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_f(v_x), t_b)),
% 0.83/0.84 inference(unit_resolution,[status(thm)],[355, 349, 339])).
% 0.83/0.84 tff(357,plain,
% 0.83/0.84 (c_less(v_f(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)),
% 0.83/0.84 inference(unit_resolution,[status(thm)],[356, 325])).
% 0.83/0.84 tff(358,plain,
% 0.83/0.84 (^[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))))),
% 0.83/0.84 inference(bind,[status(th)],[])).
% 0.83/0.84 tff(359,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(quant_intro,[status(thm)],[358])).
% 0.83/0.84 tff(360,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(361,plain,
% 0.83/0.84 (^[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))))),
% 0.83/0.84 inference(bind,[status(th)],[])).
% 0.83/0.84 tff(362,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(quant_intro,[status(thm)],[361])).
% 0.83/0.84 tff(363,axiom,(![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_LOrder_Ojoin__semilorder(T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clsrel_Ring__and__Field_Oordered__idom_35')).
% 0.83/0.84 tff(364,plain,
% 0.83/0.84 (![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.83/0.84 tff(365,plain,
% 0.83/0.84 (![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[364, 360])).
% 0.83/0.84 tff(366,plain,(
% 0.83/0.84 ![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.84 inference(skolemize,[status(sab)],[365])).
% 0.83/0.84 tff(367,plain,
% 0.83/0.84 (![T: $i] : (class_LOrder_Ojoin__semilorder(T) | (~class_Ring__and__Field_Oordered__idom(T)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[366, 359])).
% 0.83/0.84 tff(368,plain,
% 0.83/0.84 (((~![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)))),
% 0.83/0.84 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(369,plain,
% 0.83/0.84 ((~![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)))),
% 0.83/0.84 inference(quant_inst,[status(thm)],[])).
% 0.83/0.84 tff(370,plain,
% 0.83/0.84 ((~![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))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.83/0.84 tff(371,plain,
% 0.83/0.84 (class_LOrder_Ojoin__semilorder(t_b)),
% 0.83/0.84 inference(unit_resolution,[status(thm)],[370, 13, 367])).
% 0.83/0.84 tff(372,plain,
% 0.83/0.84 (^[T: $i] : refl((class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T))) <=> (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T))))),
% 0.83/0.84 inference(bind,[status(th)],[])).
% 0.83/0.84 tff(373,plain,
% 0.83/0.84 (![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T))) <=> ![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 0.83/0.84 inference(quant_intro,[status(thm)],[372])).
% 0.83/0.84 tff(374,plain,
% 0.83/0.84 (![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T))) <=> ![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 0.83/0.84 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(375,plain,
% 0.83/0.84 (^[T: $i] : rewrite(((~class_LOrder_Ojoin__semilorder(T)) | class_Orderings_Oorder(T)) <=> (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T))))),
% 0.83/0.84 inference(bind,[status(th)],[])).
% 0.83/0.84 tff(376,plain,
% 0.83/0.84 (![T: $i] : ((~class_LOrder_Ojoin__semilorder(T)) | class_Orderings_Oorder(T)) <=> ![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 0.83/0.84 inference(quant_intro,[status(thm)],[375])).
% 0.83/0.84 tff(377,axiom,(![T: $i] : ((~class_LOrder_Ojoin__semilorder(T)) | class_Orderings_Oorder(T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clsrel_LOrder_Ojoin__semilorder_1')).
% 0.83/0.84 tff(378,plain,
% 0.83/0.84 (![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.83/0.84 tff(379,plain,
% 0.83/0.84 (![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[378, 374])).
% 0.83/0.84 tff(380,plain,(
% 0.83/0.84 ![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 0.83/0.84 inference(skolemize,[status(sab)],[379])).
% 0.83/0.84 tff(381,plain,
% 0.83/0.84 (![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[380, 373])).
% 0.83/0.84 tff(382,plain,
% 0.83/0.84 (((~![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)))),
% 0.83/0.84 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(383,plain,
% 0.83/0.84 ((~![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))) | (class_Orderings_Oorder(t_b) | (~class_LOrder_Ojoin__semilorder(t_b)))),
% 0.83/0.84 inference(quant_inst,[status(thm)],[])).
% 0.83/0.84 tff(384,plain,
% 0.83/0.84 ((~![T: $i] : (class_Orderings_Oorder(T) | (~class_LOrder_Ojoin__semilorder(T)))) | class_Orderings_Oorder(t_b) | (~class_LOrder_Ojoin__semilorder(t_b))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.83/0.84 tff(385,plain,
% 0.83/0.84 (class_Orderings_Oorder(t_b)),
% 0.83/0.84 inference(unit_resolution,[status(thm)],[384, 381, 371])).
% 0.83/0.84 tff(386,plain,
% 0.83/0.84 (^[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))))),
% 0.83/0.84 inference(bind,[status(th)],[])).
% 0.83/0.84 tff(387,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(quant_intro,[status(thm)],[386])).
% 0.83/0.84 tff(388,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(389,plain,
% 0.83/0.84 (^[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))))),
% 0.83/0.84 inference(bind,[status(th)],[])).
% 0.83/0.84 tff(390,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(quant_intro,[status(thm)],[389])).
% 0.83/0.84 tff(391,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/sandbox/benchmark/theBenchmark.p','cls_Orderings_Oorder__less__imp__le_0')).
% 0.83/0.84 tff(392,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.83/0.84 tff(393,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[392, 388])).
% 0.83/0.84 tff(394,plain,(
% 0.83/0.84 ![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)))),
% 0.83/0.84 inference(skolemize,[status(sab)],[393])).
% 0.83/0.84 tff(395,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[394, 387])).
% 0.83/0.84 tff(396,plain,
% 0.83/0.84 (((~![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_f(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_less(v_f(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_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_f(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_less(v_f(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)))),
% 0.83/0.84 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(397,plain,
% 0.83/0.84 ((c_lessequals(v_f(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_less(v_f(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_Orderings_Oorder(t_b))) <=> ((~class_Orderings_Oorder(t_b)) | c_lessequals(v_f(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_less(v_f(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)))),
% 0.83/0.84 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(398,plain,
% 0.83/0.84 (((~![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_f(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_less(v_f(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_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_f(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_less(v_f(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))))),
% 0.83/0.84 inference(monotonicity,[status(thm)],[397])).
% 0.83/0.84 tff(399,plain,
% 0.83/0.84 (((~![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_f(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_less(v_f(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_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_f(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_less(v_f(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)))),
% 0.83/0.84 inference(transitivity,[status(thm)],[398, 396])).
% 0.83/0.84 tff(400,plain,
% 0.83/0.84 ((~![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_f(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_less(v_f(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_Orderings_Oorder(t_b)))),
% 0.83/0.84 inference(quant_inst,[status(thm)],[])).
% 0.83/0.84 tff(401,plain,
% 0.83/0.84 ((~![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_f(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_less(v_f(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))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.83/0.84 tff(402,plain,
% 0.83/0.84 (c_lessequals(v_f(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)),
% 0.83/0.84 inference(unit_resolution,[status(thm)],[401, 395, 385, 357])).
% 0.83/0.84 tff(403,plain,
% 0.83/0.84 (c_lessequals(v_f(v_x), v_g(v_x), t_b)),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[402, 291])).
% 0.83/0.84 tff(404,plain,
% 0.83/0.84 (((~![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)))),
% 0.83/0.84 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(405,plain,
% 0.83/0.84 ((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)))),
% 0.83/0.84 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(406,plain,
% 0.83/0.84 (((~![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))))),
% 0.83/0.84 inference(monotonicity,[status(thm)],[405])).
% 0.83/0.84 tff(407,plain,
% 0.83/0.84 (((~![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)))),
% 0.83/0.84 inference(transitivity,[status(thm)],[406, 404])).
% 0.83/0.84 tff(408,plain,
% 0.83/0.84 ((~![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)))),
% 0.83/0.84 inference(quant_inst,[status(thm)],[])).
% 0.83/0.84 tff(409,plain,
% 0.83/0.84 ((~![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))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.83/0.84 tff(410,plain,
% 0.83/0.84 (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))),
% 0.83/0.84 inference(unit_resolution,[status(thm)],[409, 316])).
% 0.83/0.84 tff(411,plain,
% 0.83/0.84 (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))),
% 0.83/0.84 inference(unit_resolution,[status(thm)],[410, 306])).
% 0.83/0.84 tff(412,plain,
% 0.83/0.84 (c_lessequals(c_minus(v_f(v_x), v_g(v_x), t_b), c_0, t_b)),
% 0.83/0.84 inference(unit_resolution,[status(thm)],[411, 403])).
% 0.83/0.84 tff(413,plain,
% 0.83/0.84 (^[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))))),
% 0.83/0.84 inference(bind,[status(th)],[])).
% 0.83/0.84 tff(414,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(quant_intro,[status(thm)],[413])).
% 0.83/0.84 tff(415,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(416,plain,
% 0.83/0.84 (^[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))))),
% 0.83/0.84 inference(bind,[status(th)],[])).
% 0.83/0.84 tff(417,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(quant_intro,[status(thm)],[416])).
% 0.83/0.84 tff(418,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/sandbox/benchmark/theBenchmark.p','cls_OrderedGroup_Oabs__of__nonpos_0')).
% 0.83/0.84 tff(419,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.83/0.84 tff(420,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[419, 415])).
% 0.83/0.84 tff(421,plain,(
% 0.83/0.84 ![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)))),
% 0.83/0.84 inference(skolemize,[status(sab)],[420])).
% 0.83/0.84 tff(422,plain,
% 0.83/0.84 (![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)))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[421, 414])).
% 0.83/0.84 tff(423,plain,
% 0.83/0.84 (((~![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)))),
% 0.83/0.84 inference(rewrite,[status(thm)],[])).
% 0.83/0.84 tff(424,plain,
% 0.83/0.84 ((~![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)))),
% 0.83/0.84 inference(quant_inst,[status(thm)],[])).
% 0.83/0.84 tff(425,plain,
% 0.83/0.84 ((~![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))),
% 0.83/0.84 inference(modus_ponens,[status(thm)],[424, 423])).
% 0.83/0.84 tff(426,plain,
% 0.83/0.84 ((~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))),
% 0.83/0.84 inference(unit_resolution,[status(thm)],[425, 422])).
% 0.83/0.84 tff(427,plain,
% 0.83/0.84 ((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))),
% 0.83/0.84 inference(unit_resolution,[status(thm)],[426, 150])).
% 0.83/0.84 tff(428,plain,
% 0.83/0.84 (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)),
% 0.83/0.84 inference(unit_resolution,[status(thm)],[427, 412])).
% 0.83/0.84 tff(429,plain,
% 0.83/0.84 (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)),
% 0.83/0.84 inference(transitivity,[status(thm)],[428, 290])).
% 0.83/0.84 tff(430,plain,
% 0.83/0.84 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 0.83/0.84 inference(monotonicity,[status(thm)],[429])).
% 0.83/0.84 tff(431,plain,
% 0.83/0.84 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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_minus(v_f(v_x), v_g(v_x), t_b)),
% 0.91/0.85 inference(transitivity,[status(thm)],[430, 285, 280, 133])).
% 0.91/0.85 tff(432,plain,
% 0.91/0.85 (c_plus(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_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_plus(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(v_f(v_x), v_g(v_x), t_b), t_b)),
% 0.91/0.85 inference(monotonicity,[status(thm)],[431])).
% 0.91/0.85 tff(433,plain,
% 0.91/0.85 (((~![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_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_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_plus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), 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_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_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_plus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))),
% 0.91/0.85 inference(rewrite,[status(thm)],[])).
% 0.91/0.85 tff(434,plain,
% 0.91/0.85 ((~![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_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_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_plus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))),
% 0.91/0.85 inference(quant_inst,[status(thm)],[])).
% 0.91/0.85 tff(435,plain,
% 0.91/0.85 ((~![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_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_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_plus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b))),
% 0.91/0.85 inference(modus_ponens,[status(thm)],[434, 433])).
% 0.91/0.85 tff(436,plain,
% 0.91/0.85 (c_plus(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_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = c_minus(c_plus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[435, 122, 17])).
% 0.91/0.85 tff(437,plain,
% 0.91/0.85 (c_minus(c_plus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_plus(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_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b)),
% 0.91/0.85 inference(symmetry,[status(thm)],[436])).
% 0.91/0.85 tff(438,plain,
% 0.91/0.85 (((~![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_plus(c_uminus(v_g(v_x), t_b), 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), t_b) = c_plus(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_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_plus(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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.91/0.85 inference(rewrite,[status(thm)],[])).
% 0.91/0.85 tff(439,plain,
% 0.91/0.85 ((~![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_plus(c_uminus(v_g(v_x), t_b), 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), t_b) = c_plus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.91/0.85 inference(quant_inst,[status(thm)],[])).
% 0.91/0.85 tff(440,plain,
% 0.91/0.85 ((~![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_plus(c_uminus(v_g(v_x), t_b), 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), t_b) = c_plus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 0.91/0.85 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.91/0.85 tff(441,plain,
% 0.91/0.85 (c_minus(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_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_plus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[440, 24, 17])).
% 0.91/0.85 tff(442,plain,
% 0.91/0.85 (c_minus(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_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b) = c_minus(v_g(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.91/0.85 inference(monotonicity,[status(thm)],[164, 230])).
% 0.91/0.85 tff(443,plain,
% 0.91/0.85 (c_minus(v_g(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(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_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 0.91/0.85 inference(symmetry,[status(thm)],[442])).
% 0.91/0.85 tff(444,plain,
% 0.91/0.85 (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)),
% 0.91/0.85 inference(symmetry,[status(thm)],[252])).
% 0.91/0.85 tff(445,plain,
% 0.91/0.85 (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)),
% 0.91/0.85 inference(symmetry,[status(thm)],[250])).
% 0.91/0.85 tff(446,plain,
% 0.91/0.85 (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_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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.91/0.85 inference(transitivity,[status(thm)],[33, 445, 444, 265, 443, 441])).
% 0.91/0.85 tff(447,plain,
% 0.91/0.85 (c_minus(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_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_minus(c_plus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 0.91/0.85 inference(monotonicity,[status(thm)],[446])).
% 0.91/0.85 tff(448,plain,
% 0.91/0.85 (c_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_minus(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_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 0.91/0.85 inference(monotonicity,[status(thm)],[165])).
% 0.91/0.85 tff(449,plain,
% 0.91/0.85 (((~![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_plus(c_uminus(v_g(v_x), t_b), 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_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_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), 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_plus(c_uminus(v_g(v_x), t_b), 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_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_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))),
% 0.91/0.85 inference(rewrite,[status(thm)],[])).
% 0.91/0.85 tff(450,plain,
% 0.91/0.85 ((~![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_plus(c_uminus(v_g(v_x), t_b), 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_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_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)))),
% 0.91/0.85 inference(quant_inst,[status(thm)],[])).
% 0.91/0.85 tff(451,plain,
% 0.91/0.85 ((~![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_plus(c_uminus(v_g(v_x), t_b), 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_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_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b))),
% 0.91/0.85 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.91/0.85 tff(452,plain,
% 0.91/0.85 (c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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_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_minus(c_plus(c_plus(c_uminus(v_g(v_x), t_b), 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), t_b), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[451, 197, 17])).
% 0.91/0.85 tff(453,plain,
% 0.91/0.85 (c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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), c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 0.91/0.85 inference(symmetry,[status(thm)],[430])).
% 0.91/0.85 tff(454,plain,
% 0.91/0.85 (c_uminus(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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 0.91/0.85 inference(symmetry,[status(thm)],[280])).
% 0.91/0.85 tff(455,plain,
% 0.91/0.85 (c_minus(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_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 0.91/0.85 inference(transitivity,[status(thm)],[134, 454, 284, 453])).
% 0.91/0.85 tff(456,plain,
% 0.91/0.85 (c_plus(c_minus(v_f(v_x), 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), t_b) = c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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_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)),
% 0.91/0.85 inference(monotonicity,[status(thm)],[455])).
% 0.91/0.85 tff(457,plain,
% 0.91/0.85 (c_plus(c_minus(v_f(v_x), 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), t_b) = v_f(v_x)),
% 0.91/0.85 inference(transitivity,[status(thm)],[456, 452, 448, 447, 437, 432, 257, 224, 220, 202, 190, 188, 186])).
% 0.91/0.85 tff(458,plain,
% 0.91/0.85 (c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = c_minus(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_f(v_x), t_b)),
% 0.91/0.85 inference(transitivity,[status(thm)],[428, 290, 173])).
% 0.91/0.85 tff(459,plain,
% 0.91/0.85 (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_plus(c_minus(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_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)),
% 0.91/0.85 inference(monotonicity,[status(thm)],[458, 97])).
% 0.91/0.85 tff(460,plain,
% 0.91/0.85 (c_plus(c_minus(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_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_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b)),
% 0.91/0.85 inference(symmetry,[status(thm)],[459])).
% 0.91/0.85 tff(461,plain,
% 0.91/0.85 (c_plus(c_minus(v_g(v_x), 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_plus(c_minus(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_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)),
% 0.91/0.85 inference(monotonicity,[status(thm)],[173])).
% 0.91/0.85 tff(462,plain,
% 0.91/0.85 (c_plus(c_minus(v_g(v_x), 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_plus(c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), v_g(v_x), t_b)),
% 0.91/0.85 inference(transitivity,[status(thm)],[461, 460])).
% 0.91/0.85 tff(463,plain,
% 0.91/0.85 (c_lessequals(c_plus(c_minus(v_g(v_x), 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_plus(c_minus(v_f(v_x), 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), t_b), t_b) <=> c_lessequals(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_f(v_x), t_b)),
% 0.91/0.85 inference(monotonicity,[status(thm)],[462, 457])).
% 0.91/0.85 tff(464,plain,
% 0.91/0.85 (c_lessequals(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_f(v_x), t_b) <=> c_lessequals(c_plus(c_minus(v_g(v_x), 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_plus(c_minus(v_f(v_x), 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), t_b), t_b)),
% 0.91/0.85 inference(symmetry,[status(thm)],[463])).
% 0.91/0.85 tff(465,plain,
% 0.91/0.85 (^[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)))),
% 0.91/0.85 inference(bind,[status(th)],[])).
% 0.91/0.85 tff(466,plain,
% 0.91/0.85 (![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))),
% 0.91/0.85 inference(quant_intro,[status(thm)],[465])).
% 0.91/0.85 tff(467,plain,
% 0.91/0.85 (![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))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(468,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/sandbox/benchmark/theBenchmark.p','cls_OrderedGroup_Oabs__ge__zero_0')).
% 0.91/0.86 tff(469,plain,
% 0.91/0.86 (![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))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.91/0.86 tff(470,plain,(
% 0.91/0.86 ![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))),
% 0.91/0.86 inference(skolemize,[status(sab)],[469])).
% 0.91/0.86 tff(471,plain,
% 0.91/0.86 (![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))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[470, 466])).
% 0.91/0.86 tff(472,plain,
% 0.91/0.86 (((~![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))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(473,plain,
% 0.91/0.86 ((~![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))),
% 0.91/0.86 inference(quant_inst,[status(thm)],[])).
% 0.91/0.86 tff(474,plain,
% 0.91/0.86 ((~![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)),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.91/0.86 tff(475,plain,
% 0.91/0.86 ((~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)),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[474, 471])).
% 0.91/0.86 tff(476,plain,
% 0.91/0.86 (c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[475, 150])).
% 0.91/0.86 tff(477,plain,
% 0.91/0.86 (^[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))))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(478,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(quant_intro,[status(thm)],[477])).
% 0.91/0.86 tff(479,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(480,plain,
% 0.91/0.86 (^[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)))))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(481,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(quant_intro,[status(thm)],[480])).
% 0.91/0.86 tff(482,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/sandbox/benchmark/theBenchmark.p','cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2')).
% 0.91/0.86 tff(483,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.91/0.86 tff(484,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[483, 479])).
% 0.91/0.86 tff(485,plain,(
% 0.91/0.86 ![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)))),
% 0.91/0.86 inference(skolemize,[status(sab)],[484])).
% 0.91/0.86 tff(486,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[485, 478])).
% 0.91/0.86 tff(487,plain,
% 0.91/0.86 ((~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))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(488,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/sandbox/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.91/0.86 tff(489,plain,
% 0.91/0.86 (~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)),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.91/0.86 tff(490,plain,
% 0.91/0.86 (((~![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)))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(491,plain,
% 0.91/0.86 ((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)))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(492,plain,
% 0.91/0.86 (((~![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))))),
% 0.91/0.86 inference(monotonicity,[status(thm)],[491])).
% 0.91/0.86 tff(493,plain,
% 0.91/0.86 (((~![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)))),
% 0.91/0.86 inference(transitivity,[status(thm)],[492, 490])).
% 0.91/0.86 tff(494,plain,
% 0.91/0.86 ((~![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)))),
% 0.91/0.86 inference(quant_inst,[status(thm)],[])).
% 0.91/0.86 tff(495,plain,
% 0.91/0.86 ((~![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))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.91/0.86 tff(496,plain,
% 0.91/0.86 ((~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))),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[495, 489, 486])).
% 0.91/0.86 tff(497,plain,
% 0.91/0.86 (~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)),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[496, 476, 339])).
% 0.91/0.86 tff(498,plain,
% 0.91/0.86 (^[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))))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(499,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(quant_intro,[status(thm)],[498])).
% 0.91/0.86 tff(500,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(501,plain,
% 0.91/0.86 (^[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))))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(502,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(quant_intro,[status(thm)],[501])).
% 0.91/0.86 tff(503,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/sandbox/benchmark/theBenchmark.p','cls_OrderedGroup_Ocompare__rls__8_1')).
% 0.91/0.86 tff(504,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.91/0.86 tff(505,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[504, 500])).
% 0.91/0.86 tff(506,plain,(
% 0.91/0.86 ![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)))),
% 0.91/0.86 inference(skolemize,[status(sab)],[505])).
% 0.91/0.86 tff(507,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[506, 499])).
% 0.91/0.86 tff(508,plain,
% 0.91/0.86 (((~![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)))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(509,plain,
% 0.91/0.86 ((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)))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(510,plain,
% 0.91/0.86 (((~![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))))),
% 0.91/0.86 inference(monotonicity,[status(thm)],[509])).
% 0.91/0.86 tff(511,plain,
% 0.91/0.86 (((~![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)))),
% 0.91/0.86 inference(transitivity,[status(thm)],[510, 508])).
% 0.91/0.86 tff(512,plain,
% 0.91/0.86 ((~![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)))),
% 0.91/0.86 inference(quant_inst,[status(thm)],[])).
% 0.91/0.86 tff(513,plain,
% 0.91/0.86 ((~![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))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.91/0.86 tff(514,plain,
% 0.91/0.86 ((~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))),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[513, 507, 497])).
% 0.91/0.86 tff(515,plain,
% 0.91/0.86 (~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)),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[514, 306])).
% 0.91/0.86 tff(516,plain,
% 0.91/0.86 (^[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))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(517,plain,
% 0.91/0.86 (![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)),
% 0.91/0.86 inference(quant_intro,[status(thm)],[516])).
% 0.91/0.86 tff(518,plain,
% 0.91/0.86 (![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)),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(519,axiom,(![V_U: $i] : c_lessequals(v_k(V_U), v_f(V_U), t_b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.91/0.86 tff(520,plain,
% 0.91/0.86 (![V_U: $i] : c_lessequals(v_k(V_U), v_f(V_U), t_b)),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[519, 518])).
% 0.91/0.86 tff(521,plain,(
% 0.91/0.86 ![V_U: $i] : c_lessequals(v_k(V_U), v_f(V_U), t_b)),
% 0.91/0.86 inference(skolemize,[status(sab)],[520])).
% 0.91/0.86 tff(522,plain,
% 0.91/0.86 (![V_U: $i] : c_lessequals(v_k(V_U), v_f(V_U), t_b)),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[521, 517])).
% 0.91/0.86 tff(523,plain,
% 0.91/0.86 ((~![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)),
% 0.91/0.86 inference(quant_inst,[status(thm)],[])).
% 0.91/0.86 tff(524,plain,
% 0.91/0.86 (c_lessequals(v_k(v_x), v_f(v_x), t_b)),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[523, 522])).
% 0.91/0.86 tff(525,plain,
% 0.91/0.86 (^[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))))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(526,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(quant_intro,[status(thm)],[525])).
% 0.91/0.86 tff(527,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(528,plain,
% 0.91/0.86 (^[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)))))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(529,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(quant_intro,[status(thm)],[528])).
% 0.91/0.86 tff(530,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/sandbox/benchmark/theBenchmark.p','cls_Orderings_Oorder__class_Oorder__trans_0')).
% 0.91/0.86 tff(531,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.91/0.86 tff(532,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[531, 527])).
% 0.91/0.86 tff(533,plain,(
% 0.91/0.86 ![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)))),
% 0.91/0.86 inference(skolemize,[status(sab)],[532])).
% 0.91/0.86 tff(534,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[533, 526])).
% 0.91/0.86 tff(535,plain,
% 0.91/0.86 (((~![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_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)) | (~c_lessequals(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), 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_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)) | (~c_lessequals(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), t_b)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(536,plain,
% 0.93/0.87 ((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)) | (~c_lessequals(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), t_b)) | (~class_Orderings_Oorder(t_b))) <=> ((~class_Orderings_Oorder(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) | (~c_lessequals(v_k(v_x), v_f(v_x), t_b)) | (~c_lessequals(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), t_b)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(537,plain,
% 0.93/0.87 (((~![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_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)) | (~c_lessequals(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), 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_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)) | (~c_lessequals(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), t_b))))),
% 0.93/0.87 inference(monotonicity,[status(thm)],[536])).
% 0.93/0.87 tff(538,plain,
% 0.93/0.87 (((~![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_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)) | (~c_lessequals(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), 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_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)) | (~c_lessequals(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), t_b)))),
% 0.93/0.87 inference(transitivity,[status(thm)],[537, 535])).
% 0.93/0.87 tff(539,plain,
% 0.93/0.87 ((~![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_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)) | (~c_lessequals(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), t_b)) | (~class_Orderings_Oorder(t_b)))),
% 0.93/0.87 inference(quant_inst,[status(thm)],[])).
% 0.93/0.87 tff(540,plain,
% 0.93/0.87 ((~![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_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)) | (~c_lessequals(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), t_b))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[539, 538])).
% 0.93/0.87 tff(541,plain,
% 0.93/0.87 (~c_lessequals(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), t_b)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[540, 534, 524, 385, 515])).
% 0.93/0.87 tff(542,plain,
% 0.93/0.87 (((~![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_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), t_b) | (~c_less(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), 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_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), t_b) | (~c_less(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), t_b)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(543,plain,
% 0.93/0.87 ((c_lessequals(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), t_b) | (~c_less(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), t_b)) | (~class_Orderings_Oorder(t_b))) <=> ((~class_Orderings_Oorder(t_b)) | c_lessequals(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), t_b) | (~c_less(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), t_b)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(544,plain,
% 0.93/0.87 (((~![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_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), t_b) | (~c_less(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), 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_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), t_b) | (~c_less(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), t_b))))),
% 0.93/0.87 inference(monotonicity,[status(thm)],[543])).
% 0.93/0.87 tff(545,plain,
% 0.93/0.87 (((~![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_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), t_b) | (~c_less(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), 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_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), t_b) | (~c_less(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), t_b)))),
% 0.93/0.87 inference(transitivity,[status(thm)],[544, 542])).
% 0.93/0.87 tff(546,plain,
% 0.93/0.87 ((~![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_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), t_b) | (~c_less(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), t_b)) | (~class_Orderings_Oorder(t_b)))),
% 0.93/0.87 inference(quant_inst,[status(thm)],[])).
% 0.93/0.87 tff(547,plain,
% 0.93/0.87 ((~![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_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), t_b) | (~c_less(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), t_b))),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.93/0.87 tff(548,plain,
% 0.93/0.87 (~c_less(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), t_b)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[547, 395, 385, 541])).
% 0.93/0.87 tff(549,plain,
% 0.93/0.87 (((~![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_less(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), t_b) | c_lessequals(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_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_less(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), t_b) | c_lessequals(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_f(v_x), t_b))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(550,plain,
% 0.93/0.87 ((c_lessequals(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_f(v_x), t_b) | c_less(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), t_b) | (~class_Orderings_Olinorder(t_b))) <=> ((~class_Orderings_Olinorder(t_b)) | c_less(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), t_b) | c_lessequals(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_f(v_x), t_b))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(551,plain,
% 0.93/0.87 (((~![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_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_f(v_x), t_b) | c_less(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), 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_less(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), t_b) | c_lessequals(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_f(v_x), t_b)))),
% 0.93/0.87 inference(monotonicity,[status(thm)],[550])).
% 0.93/0.87 tff(552,plain,
% 0.93/0.87 (((~![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_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_f(v_x), t_b) | c_less(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), 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_less(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), t_b) | c_lessequals(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_f(v_x), t_b))),
% 0.93/0.87 inference(transitivity,[status(thm)],[551, 549])).
% 0.93/0.87 tff(553,plain,
% 0.93/0.87 ((~![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_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_f(v_x), t_b) | c_less(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), t_b) | (~class_Orderings_Olinorder(t_b)))),
% 0.93/0.87 inference(quant_inst,[status(thm)],[])).
% 0.93/0.87 tff(554,plain,
% 0.93/0.87 ((~![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_less(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), t_b) | c_lessequals(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_f(v_x), t_b)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[553, 552])).
% 0.93/0.87 tff(555,plain,
% 0.93/0.87 (c_lessequals(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_f(v_x), t_b)),
% 0.93/0.87 inference(unit_resolution,[status(thm)],[554, 349, 339, 548])).
% 0.93/0.87 tff(556,plain,
% 0.93/0.87 (c_lessequals(c_plus(c_minus(v_g(v_x), 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_plus(c_minus(v_f(v_x), 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), t_b), t_b)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[555, 464])).
% 0.93/0.87 tff(557,plain,
% 0.93/0.87 (c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b) = c_0),
% 0.93/0.87 inference(transitivity,[status(thm)],[107, 48])).
% 0.93/0.87 tff(558,plain,
% 0.93/0.87 (c_lessequals(c_minus(v_g(v_x), v_f(v_x), 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)),
% 0.93/0.87 inference(monotonicity,[status(thm)],[557])).
% 0.93/0.87 tff(559,plain,
% 0.93/0.87 (c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) <=> c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.93/0.87 inference(symmetry,[status(thm)],[558])).
% 0.93/0.87 tff(560,plain,
% 0.93/0.87 ((~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b)) <=> (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 0.93/0.87 inference(monotonicity,[status(thm)],[559])).
% 0.93/0.87 tff(561,plain,
% 0.93/0.87 (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.93/0.87 inference(modus_ponens,[status(thm)],[295, 560])).
% 0.93/0.87 tff(562,plain,
% 0.93/0.87 (((~![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_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_less(c_minus(v_g(v_x), v_f(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, 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_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(563,plain,
% 0.93/0.87 ((c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_less(c_minus(v_g(v_x), v_f(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_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.93/0.87 inference(rewrite,[status(thm)],[])).
% 0.93/0.87 tff(564,plain,
% 0.93/0.87 (((~![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_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_less(c_minus(v_g(v_x), v_f(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, 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_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))))),
% 0.93/0.87 inference(monotonicity,[status(thm)],[563])).
% 0.93/0.87 tff(565,plain,
% 0.93/0.87 (((~![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_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_less(c_minus(v_g(v_x), v_f(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, 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_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.93/0.88 inference(transitivity,[status(thm)],[564, 562])).
% 0.93/0.88 tff(566,plain,
% 0.93/0.88 ((~![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_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_less(c_minus(v_g(v_x), v_f(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)))),
% 0.93/0.88 inference(quant_inst,[status(thm)],[])).
% 0.93/0.88 tff(567,plain,
% 0.93/0.88 ((~![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_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~c_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[566, 565])).
% 0.93/0.88 tff(568,plain,
% 0.93/0.88 (~c_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[567, 395, 385, 561])).
% 0.93/0.88 tff(569,plain,
% 0.93/0.88 (((~![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_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(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_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(570,plain,
% 0.93/0.88 ((c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) | c_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~class_Orderings_Olinorder(t_b))) <=> ((~class_Orderings_Olinorder(t_b)) | c_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(571,plain,
% 0.93/0.88 (((~![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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) | c_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), 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_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 0.93/0.88 inference(monotonicity,[status(thm)],[570])).
% 0.93/0.88 tff(572,plain,
% 0.93/0.88 (((~![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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) | c_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), 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_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b))),
% 0.93/0.88 inference(transitivity,[status(thm)],[571, 569])).
% 0.93/0.88 tff(573,plain,
% 0.93/0.88 ((~![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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b) | c_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | (~class_Orderings_Olinorder(t_b)))),
% 0.93/0.88 inference(quant_inst,[status(thm)],[])).
% 0.93/0.88 tff(574,plain,
% 0.93/0.88 ((~![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_less(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) | c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.93/0.88 tff(575,plain,
% 0.93/0.88 (c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[574, 349, 339, 568])).
% 0.93/0.88 tff(576,plain,
% 0.93/0.88 (((~![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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(577,plain,
% 0.93/0.88 ((c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), 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_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b))) <=> ((~class_Orderings_Oorder(t_b)) | c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(578,plain,
% 0.93/0.88 (((~![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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), 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_minus(v_f(v_x), 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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b))))),
% 0.93/0.88 inference(monotonicity,[status(thm)],[577])).
% 0.93/0.88 tff(579,plain,
% 0.93/0.88 (((~![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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), 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_minus(v_f(v_x), 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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b)))),
% 0.93/0.88 inference(transitivity,[status(thm)],[578, 576])).
% 0.93/0.88 tff(580,plain,
% 0.93/0.88 ((~![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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), 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_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~class_Orderings_Oorder(t_b)))),
% 0.93/0.88 inference(quant_inst,[status(thm)],[])).
% 0.93/0.88 tff(581,plain,
% 0.93/0.88 ((~![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_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_g(v_x), v_f(v_x), t_b), t_b))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.93/0.88 tff(582,plain,
% 0.93/0.88 (~c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[581, 534, 385, 182, 575])).
% 0.93/0.88 tff(583,plain,
% 0.93/0.88 (^[T: $i] : refl(((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)) <=> ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)))),
% 0.93/0.88 inference(bind,[status(th)],[])).
% 0.93/0.88 tff(584,plain,
% 0.93/0.88 (![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)) <=> ![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T))),
% 0.93/0.88 inference(quant_intro,[status(thm)],[583])).
% 0.93/0.88 tff(585,plain,
% 0.93/0.88 (![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)) <=> ![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(586,axiom,(![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clsrel_OrderedGroup_Olordered__ab__group__abs_6')).
% 0.93/0.88 tff(587,plain,
% 0.93/0.88 (![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.93/0.88 tff(588,plain,(
% 0.93/0.88 ![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T))),
% 0.93/0.88 inference(skolemize,[status(sab)],[587])).
% 0.93/0.88 tff(589,plain,
% 0.93/0.88 (![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[588, 584])).
% 0.93/0.88 tff(590,plain,
% 0.93/0.88 (((~![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b))) <=> ((~![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(591,plain,
% 0.93/0.88 ((~![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b))),
% 0.93/0.88 inference(quant_inst,[status(thm)],[])).
% 0.93/0.88 tff(592,plain,
% 0.93/0.88 ((~![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.93/0.88 tff(593,plain,
% 0.93/0.88 (class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[592, 589, 150])).
% 0.93/0.88 tff(594,plain,
% 0.93/0.88 (^[V_c: $i, V_b: $i, V_a: $i, T_a: $i] : refl((c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a))) <=> (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a))))),
% 0.93/0.88 inference(bind,[status(th)],[])).
% 0.93/0.88 tff(595,plain,
% 0.93/0.88 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a))) <=> ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))),
% 0.93/0.88 inference(quant_intro,[status(thm)],[594])).
% 0.93/0.88 tff(596,plain,
% 0.93/0.88 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a))) <=> ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(597,plain,
% 0.93/0.88 (^[V_c: $i, V_b: $i, V_a: $i, T_a: $i] : rewrite((((~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a))) | c_lessequals(V_a, V_b, T_a)) <=> (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a))))),
% 0.93/0.88 inference(bind,[status(th)],[])).
% 0.93/0.88 tff(598,plain,
% 0.93/0.88 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (((~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a))) | c_lessequals(V_a, V_b, T_a)) <=> ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))),
% 0.93/0.88 inference(quant_intro,[status(thm)],[597])).
% 0.93/0.88 tff(599,axiom,(![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (((~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a))) | c_lessequals(V_a, V_b, T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_OrderedGroup_Oadd__le__cancel__right_0')).
% 0.93/0.88 tff(600,plain,
% 0.93/0.88 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[599, 598])).
% 0.93/0.88 tff(601,plain,
% 0.93/0.88 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[600, 596])).
% 0.93/0.88 tff(602,plain,(
% 0.93/0.88 ![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))),
% 0.93/0.88 inference(skolemize,[status(sab)],[601])).
% 0.93/0.88 tff(603,plain,
% 0.93/0.88 (![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[602, 595])).
% 0.93/0.88 tff(604,plain,
% 0.93/0.88 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))) | ((~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)) | c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_minus(v_g(v_x), 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_plus(c_minus(v_f(v_x), 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), t_b), t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)) | c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_minus(v_g(v_x), 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_plus(c_minus(v_f(v_x), 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), t_b), t_b)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(605,plain,
% 0.93/0.88 ((c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_minus(v_g(v_x), 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_plus(c_minus(v_f(v_x), 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), t_b), t_b)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b))) <=> ((~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)) | c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_minus(v_g(v_x), 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_plus(c_minus(v_f(v_x), 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), t_b), t_b)))),
% 0.93/0.88 inference(rewrite,[status(thm)],[])).
% 0.93/0.88 tff(606,plain,
% 0.93/0.88 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))) | (c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_minus(v_g(v_x), 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_plus(c_minus(v_f(v_x), 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), t_b), t_b)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))) | ((~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)) | c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_minus(v_g(v_x), 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_plus(c_minus(v_f(v_x), 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), t_b), t_b))))),
% 0.93/0.88 inference(monotonicity,[status(thm)],[605])).
% 0.93/0.88 tff(607,plain,
% 0.93/0.88 (((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))) | (c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_minus(v_g(v_x), 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_plus(c_minus(v_f(v_x), 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), t_b), t_b)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)))) <=> ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)) | c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_minus(v_g(v_x), 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_plus(c_minus(v_f(v_x), 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), t_b), t_b)))),
% 0.93/0.88 inference(transitivity,[status(thm)],[606, 604])).
% 0.93/0.88 tff(608,plain,
% 0.93/0.88 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))) | (c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_minus(v_g(v_x), 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_plus(c_minus(v_f(v_x), 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), t_b), t_b)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)))),
% 0.93/0.88 inference(quant_inst,[status(thm)],[])).
% 0.93/0.88 tff(609,plain,
% 0.93/0.88 ((~![V_c: $i, V_b: $i, V_a: $i, T_a: $i] : (c_lessequals(V_a, V_b, T_a) | (~c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)))) | (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)) | c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) | (~c_lessequals(c_plus(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b))),
% 0.93/0.88 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.93/0.88 tff(610,plain,
% 0.93/0.88 (~c_lessequals(c_plus(c_minus(v_g(v_x), v_f(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), c_plus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[609, 603, 593, 582])).
% 0.93/0.88 tff(611,plain,
% 0.93/0.88 ($false),
% 0.93/0.88 inference(unit_resolution,[status(thm)],[610, 556])).
% 0.93/0.89 tff(612,plain,(c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b) | c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.89 tff(613,plain,
% 0.93/0.89 (c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[612, 182])).
% 0.93/0.89 tff(614,plain,
% 0.93/0.89 (((~![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)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(615,plain,
% 0.93/0.89 ((~![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)))),
% 0.93/0.89 inference(quant_inst,[status(thm)],[])).
% 0.93/0.89 tff(616,plain,
% 0.93/0.89 ((~![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))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.93/0.89 tff(617,plain,
% 0.93/0.89 ((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))),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[616, 422, 150])).
% 0.93/0.89 tff(618,plain,
% 0.93/0.89 (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)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[617, 613])).
% 0.93/0.89 tff(619,plain,
% 0.93/0.89 (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)),
% 0.93/0.89 inference(transitivity,[status(thm)],[135, 161, 618, 133])).
% 0.93/0.89 tff(620,plain,
% 0.93/0.89 (c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b) <=> c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 0.93/0.89 inference(monotonicity,[status(thm)],[50, 619])).
% 0.93/0.89 tff(621,plain,
% 0.93/0.89 (c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), 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)),
% 0.93/0.89 inference(symmetry,[status(thm)],[620])).
% 0.93/0.89 tff(622,plain,
% 0.93/0.89 ((~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), 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))),
% 0.93/0.89 inference(monotonicity,[status(thm)],[621])).
% 0.93/0.89 tff(623,plain,
% 0.93/0.89 (~c_lessequals(c_0, c_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b)),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[182, 622])).
% 0.93/0.89 tff(624,plain,
% 0.93/0.89 ($false),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[476, 623])).
% 0.93/0.89 tff(625,plain,(c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.89 tff(626,plain,
% 0.93/0.89 (((~![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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_0, t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), 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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_0, t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(627,plain,
% 0.93/0.89 ((c_lessequals(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_0, t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), 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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_0, t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(628,plain,
% 0.93/0.89 (((~![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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_0, t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), 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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_0, t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))))),
% 0.93/0.89 inference(monotonicity,[status(thm)],[627])).
% 0.93/0.89 tff(629,plain,
% 0.93/0.89 (((~![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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_0, t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), 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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_0, t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)))),
% 0.93/0.89 inference(transitivity,[status(thm)],[628, 626])).
% 0.93/0.89 tff(630,plain,
% 0.93/0.89 ((~![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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_0, t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) | (~class_OrderedGroup_Opordered__ab__group__add(t_b)))),
% 0.93/0.89 inference(quant_inst,[status(thm)],[])).
% 0.93/0.89 tff(631,plain,
% 0.93/0.89 ((~![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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_0, t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.93/0.89 tff(632,plain,
% 0.93/0.89 (c_lessequals(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_0, t_b) | (~c_lessequals(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b))),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[631, 316, 306])).
% 0.93/0.89 tff(633,plain,
% 0.93/0.89 (c_lessequals(c_minus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), c_0, t_b)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[632, 625])).
% 0.93/0.89 tff(634,plain,
% 0.93/0.89 (c_lessequals(c_minus(v_g(v_x), v_f(v_x), t_b), c_0, t_b)),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[633, 181])).
% 0.93/0.89 tff(635,plain,
% 0.93/0.89 (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)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[617, 634])).
% 0.93/0.89 tff(636,plain,
% 0.93/0.89 (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)),
% 0.93/0.89 inference(symmetry,[status(thm)],[635])).
% 0.93/0.89 tff(637,plain,
% 0.93/0.89 (v_g(v_x) = 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)),
% 0.93/0.89 inference(transitivity,[status(thm)],[77, 51, 33, 445, 444])).
% 0.93/0.89 tff(638,plain,
% 0.93/0.89 (c_minus(v_f(v_x), v_g(v_x), t_b) = c_minus(v_f(v_x), 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), t_b)),
% 0.93/0.89 inference(monotonicity,[status(thm)],[637])).
% 0.93/0.89 tff(639,plain,
% 0.93/0.89 (c_minus(v_f(v_x), 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), t_b) = c_minus(v_f(v_x), v_g(v_x), t_b)),
% 0.93/0.89 inference(symmetry,[status(thm)],[638])).
% 0.93/0.89 tff(640,plain,
% 0.93/0.89 (c_plus(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(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)),
% 0.93/0.89 inference(symmetry,[status(thm)],[246])).
% 0.93/0.89 tff(641,plain,
% 0.93/0.89 (c_plus(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_HOL_Oabs(c_minus(v_f(v_x), v_g(v_x), t_b), t_b)),
% 0.93/0.89 inference(transitivity,[status(thm)],[640, 639, 134, 636, 162, 136])).
% 0.93/0.89 tff(642,plain,
% 0.93/0.89 (c_minus(c_plus(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(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_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)),
% 0.93/0.89 inference(monotonicity,[status(thm)],[641, 128])).
% 0.93/0.89 tff(643,plain,
% 0.93/0.89 (((~![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_f(v_x), 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), t_b) = c_minus(c_plus(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(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(v_f(v_x), 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), t_b) = c_minus(c_plus(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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.93/0.89 inference(rewrite,[status(thm)],[])).
% 0.93/0.89 tff(644,plain,
% 0.93/0.89 ((~![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_f(v_x), 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), t_b) = c_minus(c_plus(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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)))),
% 0.93/0.89 inference(quant_inst,[status(thm)],[])).
% 0.93/0.89 tff(645,plain,
% 0.93/0.89 ((~![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_f(v_x), 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), t_b) = c_minus(c_plus(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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b))),
% 0.93/0.89 inference(modus_ponens,[status(thm)],[644, 643])).
% 0.93/0.89 tff(646,plain,
% 0.93/0.89 (c_plus(v_f(v_x), 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), t_b) = c_minus(c_plus(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(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), v_g(v_x), t_b), t_b)),
% 0.93/0.89 inference(unit_resolution,[status(thm)],[645, 122, 17])).
% 0.93/0.89 tff(647,plain,
% 0.93/0.89 (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)),
% 0.93/0.89 inference(monotonicity,[status(thm)],[128, 128])).
% 0.93/0.89 tff(648,plain,
% 0.93/0.89 (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)),
% 0.93/0.89 inference(symmetry,[status(thm)],[647])).
% 0.93/0.89 tff(649,plain,
% 0.93/0.89 (c_plus(c_uminus(v_g(v_x), t_b), 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)),
% 0.93/0.89 inference(transitivity,[status(thm)],[107, 648])).
% 0.93/0.89 tff(650,plain,
% 0.93/0.89 (c_plus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_plus(v_f(v_x), 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), t_b)),
% 0.93/0.89 inference(monotonicity,[status(thm)],[649])).
% 0.93/0.89 tff(651,plain,
% 0.93/0.89 (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)),
% 0.93/0.89 inference(symmetry,[status(thm)],[229])).
% 0.93/0.89 tff(652,plain,
% 0.93/0.89 (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)),
% 0.93/0.89 inference(transitivity,[status(thm)],[107, 106, 651])).
% 0.93/0.89 tff(653,plain,
% 0.93/0.89 (c_minus(v_f(v_x), c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b) = c_minus(v_f(v_x), c_uminus(c_plus(c_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b), t_b)),
% 0.93/0.89 inference(monotonicity,[status(thm)],[652])).
% 0.93/0.89 tff(654,assumption,(c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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_f(v_x), t_b) = c_minus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b)), introduced(assumption)).
% 0.93/0.89 tff(655,plain,
% 0.93/0.89 (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)),
% 0.93/0.89 inference(transitivity,[status(thm)],[216, 187, 215, 654, 204, 653, 228, 650, 646, 642, 28])).
% 0.93/0.89 tff(656,plain,
% 0.93/0.89 (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)),
% 0.93/0.90 inference(monotonicity,[status(thm)],[655])).
% 0.93/0.90 tff(657,plain,
% 0.93/0.90 (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)),
% 0.93/0.90 inference(symmetry,[status(thm)],[656])).
% 0.93/0.90 tff(658,plain,
% 0.93/0.90 ((~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))),
% 0.93/0.90 inference(monotonicity,[status(thm)],[657])).
% 0.93/0.90 tff(659,plain,
% 0.93/0.90 (~c_lessequals(v_k(v_x), v_f(v_x), t_b)),
% 0.93/0.90 inference(modus_ponens,[status(thm)],[515, 658])).
% 0.93/0.90 tff(660,plain,
% 0.93/0.90 ($false),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[524, 659])).
% 0.93/0.90 tff(661,plain,(~(c_plus(c_minus(c_plus(c_uminus(v_g(v_x), t_b), 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_f(v_x), t_b) = c_minus(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_uminus(v_g(v_x), t_b), v_g(v_x), t_b), t_b))), inference(lemma,lemma(discharge,[]))).
% 0.93/0.90 tff(662,plain,
% 0.93/0.90 ($false),
% 0.93/0.90 inference(unit_resolution,[status(thm)],[207, 197, 17, 661])).
% 0.93/0.90 % SZS output end Proof
%------------------------------------------------------------------------------