TSTP Solution File: ANA010-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA010-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 16:23:23 EDT 2022
% Result : Unsatisfiable 1.00s 0.86s
% Output : Proof 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA010-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 29 18:09:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.00/0.86 % SZS status Unsatisfiable
% 1.00/0.86 % SZS output start Proof
% 1.00/0.86 tff(c_lessequals_type, type, (
% 1.00/0.86 c_lessequals: ( $i * $i * $i ) > $o)).
% 1.00/0.86 tff(t_b_type, type, (
% 1.00/0.86 t_b: $i)).
% 1.00/0.86 tff(c_times_type, type, (
% 1.00/0.86 c_times: ( $i * $i * $i ) > $i)).
% 1.00/0.86 tff(v_g_type, type, (
% 1.00/0.86 v_g: $i > $i)).
% 1.00/0.86 tff(v_x_type, type, (
% 1.00/0.86 v_x: $i > $i)).
% 1.00/0.86 tff(c_HOL_Oabs_type, type, (
% 1.00/0.86 c_HOL_Oabs: ( $i * $i ) > $i)).
% 1.00/0.86 tff(v_c_type, type, (
% 1.00/0.86 v_c: $i)).
% 1.00/0.86 tff(v_f_type, type, (
% 1.00/0.86 v_f: $i > $i)).
% 1.00/0.86 tff(class_Ring__and__Field_Oordered__idom_type, type, (
% 1.00/0.86 class_Ring__and__Field_Oordered__idom: $i > $o)).
% 1.00/0.86 tff(c_0_type, type, (
% 1.00/0.86 c_0: $i)).
% 1.00/0.86 tff(class_Orderings_Oorder_type, type, (
% 1.00/0.86 class_Orderings_Oorder: $i > $o)).
% 1.00/0.86 tff(class_OrderedGroup_Olordered__ab__group__abs_type, type, (
% 1.00/0.86 class_OrderedGroup_Olordered__ab__group__abs: $i > $o)).
% 1.00/0.86 tff(1,plain,
% 1.00/0.86 (class_Ring__and__Field_Oordered__idom(t_b) <=> class_Ring__and__Field_Oordered__idom(t_b)),
% 1.00/0.86 inference(rewrite,[status(thm)],[])).
% 1.00/0.86 tff(2,axiom,(class_Ring__and__Field_Oordered__idom(t_b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','tfree_tcs')).
% 1.00/0.86 tff(3,plain,
% 1.00/0.86 (class_Ring__and__Field_Oordered__idom(t_b)),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[2, 1])).
% 1.00/0.86 tff(4,plain,
% 1.00/0.86 (^[V_b: $i, V_a: $i, T_a: $i] : refl(((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a))) <=> ((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a))))),
% 1.00/0.86 inference(bind,[status(th)],[])).
% 1.00/0.86 tff(5,plain,
% 1.00/0.86 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i] : ((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a)))),
% 1.00/0.86 inference(quant_intro,[status(thm)],[4])).
% 1.00/0.86 tff(6,plain,
% 1.00/0.86 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i] : ((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a)))),
% 1.00/0.86 inference(rewrite,[status(thm)],[])).
% 1.00/0.86 tff(7,axiom,(![V_b: $i, V_a: $i, T_a: $i] : ((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Ring__and__Field_Oabs__mult_0')).
% 1.00/0.86 tff(8,plain,
% 1.00/0.86 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a)))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[7, 6])).
% 1.00/0.86 tff(9,plain,(
% 1.00/0.86 ![V_b: $i, V_a: $i, T_a: $i] : ((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a)))),
% 1.00/0.86 inference(skolemize,[status(sab)],[8])).
% 1.00/0.86 tff(10,plain,
% 1.00/0.86 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a)))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[9, 5])).
% 1.00/0.86 tff(11,plain,
% 1.00/0.86 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a)))) | ((~class_Ring__and__Field_Oordered__idom(t_b)) | (c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a)))) | (~class_Ring__and__Field_Oordered__idom(t_b)) | (c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(12,plain,
% 1.00/0.87 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a)))) | ((~class_Ring__and__Field_Oordered__idom(t_b)) | (c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)))),
% 1.00/0.87 inference(quant_inst,[status(thm)],[])).
% 1.00/0.87 tff(13,plain,
% 1.00/0.87 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_Ring__and__Field_Oordered__idom(T_a)) | (c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a)))) | (~class_Ring__and__Field_Oordered__idom(t_b)) | (c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[12, 11])).
% 1.00/0.87 tff(14,plain,
% 1.00/0.87 (c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)),
% 1.00/0.87 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 1.00/0.87 tff(15,assumption,(~c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)), introduced(assumption)).
% 1.00/0.87 tff(16,plain,
% 1.00/0.87 (^[V_U: $i] : refl(c_lessequals(v_f(V_U), c_times(v_c, v_g(V_U), t_b), t_b) <=> c_lessequals(v_f(V_U), c_times(v_c, v_g(V_U), t_b), t_b))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(17,plain,
% 1.00/0.87 (![V_U: $i] : c_lessequals(v_f(V_U), c_times(v_c, v_g(V_U), t_b), t_b) <=> ![V_U: $i] : c_lessequals(v_f(V_U), c_times(v_c, v_g(V_U), t_b), t_b)),
% 1.00/0.87 inference(quant_intro,[status(thm)],[16])).
% 1.00/0.87 tff(18,plain,
% 1.00/0.87 (![V_U: $i] : c_lessequals(v_f(V_U), c_times(v_c, v_g(V_U), t_b), t_b) <=> ![V_U: $i] : c_lessequals(v_f(V_U), c_times(v_c, v_g(V_U), t_b), t_b)),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(19,axiom,(![V_U: $i] : c_lessequals(v_f(V_U), c_times(v_c, v_g(V_U), t_b), t_b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 1.00/0.87 tff(20,plain,
% 1.00/0.87 (![V_U: $i] : c_lessequals(v_f(V_U), c_times(v_c, v_g(V_U), t_b), t_b)),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.00/0.87 tff(21,plain,(
% 1.00/0.87 ![V_U: $i] : c_lessequals(v_f(V_U), c_times(v_c, v_g(V_U), t_b), t_b)),
% 1.00/0.87 inference(skolemize,[status(sab)],[20])).
% 1.00/0.87 tff(22,plain,
% 1.00/0.87 (![V_U: $i] : c_lessequals(v_f(V_U), c_times(v_c, v_g(V_U), t_b), t_b)),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[21, 17])).
% 1.00/0.87 tff(23,plain,
% 1.00/0.87 ((~![V_U: $i] : c_lessequals(v_f(V_U), c_times(v_c, v_g(V_U), t_b), t_b)) | c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)),
% 1.00/0.87 inference(quant_inst,[status(thm)],[])).
% 1.00/0.87 tff(24,plain,
% 1.00/0.87 (c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)),
% 1.00/0.87 inference(unit_resolution,[status(thm)],[23, 22])).
% 1.00/0.87 tff(25,plain,
% 1.00/0.87 (^[V_U: $i] : refl(c_lessequals(c_0, v_f(V_U), t_b) <=> c_lessequals(c_0, v_f(V_U), t_b))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(26,plain,
% 1.00/0.87 (![V_U: $i] : c_lessequals(c_0, v_f(V_U), t_b) <=> ![V_U: $i] : c_lessequals(c_0, v_f(V_U), t_b)),
% 1.00/0.87 inference(quant_intro,[status(thm)],[25])).
% 1.00/0.87 tff(27,plain,
% 1.00/0.87 (![V_U: $i] : c_lessequals(c_0, v_f(V_U), t_b) <=> ![V_U: $i] : c_lessequals(c_0, v_f(V_U), t_b)),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(28,axiom,(![V_U: $i] : c_lessequals(c_0, v_f(V_U), t_b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 1.00/0.87 tff(29,plain,
% 1.00/0.87 (![V_U: $i] : c_lessequals(c_0, v_f(V_U), t_b)),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.00/0.87 tff(30,plain,(
% 1.00/0.87 ![V_U: $i] : c_lessequals(c_0, v_f(V_U), t_b)),
% 1.00/0.87 inference(skolemize,[status(sab)],[29])).
% 1.00/0.87 tff(31,plain,
% 1.00/0.87 (![V_U: $i] : c_lessequals(c_0, v_f(V_U), t_b)),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.00/0.87 tff(32,plain,
% 1.00/0.87 ((~![V_U: $i] : c_lessequals(c_0, v_f(V_U), t_b)) | c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b)),
% 1.00/0.87 inference(quant_inst,[status(thm)],[])).
% 1.00/0.87 tff(33,plain,
% 1.00/0.87 (c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b)),
% 1.00/0.87 inference(unit_resolution,[status(thm)],[32, 31])).
% 1.00/0.87 tff(34,plain,
% 1.00/0.87 (^[T: $i] : refl(((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T)) <=> ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T)))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(35,plain,
% 1.00/0.87 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T)) <=> ![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[34])).
% 1.00/0.87 tff(36,plain,
% 1.00/0.87 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T)) <=> ![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(37,axiom,(![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsrel_Ring__and__Field_Oordered__idom_50')).
% 1.00/0.87 tff(38,plain,
% 1.00/0.87 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.00/0.87 tff(39,plain,(
% 1.00/0.87 ![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T))),
% 1.00/0.87 inference(skolemize,[status(sab)],[38])).
% 1.00/0.87 tff(40,plain,
% 1.00/0.87 (![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[39, 35])).
% 1.00/0.87 tff(41,plain,
% 1.00/0.87 (((~![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T))) | ((~class_Ring__and__Field_Oordered__idom(t_b)) | class_OrderedGroup_Olordered__ab__group__abs(t_b))) <=> ((~![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T))) | (~class_Ring__and__Field_Oordered__idom(t_b)) | class_OrderedGroup_Olordered__ab__group__abs(t_b))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(42,plain,
% 1.00/0.87 ((~![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T))) | ((~class_Ring__and__Field_Oordered__idom(t_b)) | class_OrderedGroup_Olordered__ab__group__abs(t_b))),
% 1.00/0.87 inference(quant_inst,[status(thm)],[])).
% 1.00/0.87 tff(43,plain,
% 1.00/0.87 ((~![T: $i] : ((~class_Ring__and__Field_Oordered__idom(T)) | class_OrderedGroup_Olordered__ab__group__abs(T))) | (~class_Ring__and__Field_Oordered__idom(t_b)) | class_OrderedGroup_Olordered__ab__group__abs(t_b)),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.00/0.87 tff(44,plain,
% 1.00/0.87 (class_OrderedGroup_Olordered__ab__group__abs(t_b)),
% 1.00/0.87 inference(unit_resolution,[status(thm)],[43, 40, 3])).
% 1.00/0.87 tff(45,plain,
% 1.00/0.87 (^[T: $i] : refl((class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T))) <=> (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T))))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(46,plain,
% 1.00/0.87 (![T: $i] : (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T))) <=> ![T: $i] : (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T)))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[45])).
% 1.00/0.87 tff(47,plain,
% 1.00/0.87 (![T: $i] : (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T))) <=> ![T: $i] : (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T)))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(48,plain,
% 1.00/0.87 (^[T: $i] : rewrite(((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_Orderings_Oorder(T)) <=> (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T))))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(49,plain,
% 1.00/0.87 (![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_Orderings_Oorder(T)) <=> ![T: $i] : (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T)))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[48])).
% 1.00/0.87 tff(50,axiom,(![T: $i] : ((~class_OrderedGroup_Olordered__ab__group__abs(T)) | class_Orderings_Oorder(T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsrel_OrderedGroup_Olordered__ab__group__abs_17')).
% 1.00/0.87 tff(51,plain,
% 1.00/0.87 (![T: $i] : (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T)))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.00/0.87 tff(52,plain,
% 1.00/0.87 (![T: $i] : (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T)))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[51, 47])).
% 1.00/0.87 tff(53,plain,(
% 1.00/0.87 ![T: $i] : (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T)))),
% 1.00/0.87 inference(skolemize,[status(sab)],[52])).
% 1.00/0.87 tff(54,plain,
% 1.00/0.87 (![T: $i] : (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T)))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[53, 46])).
% 1.00/0.87 tff(55,plain,
% 1.00/0.87 (((~![T: $i] : (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T)))) | (class_Orderings_Oorder(t_b) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)))) <=> ((~![T: $i] : (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T)))) | class_Orderings_Oorder(t_b) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(56,plain,
% 1.00/0.87 ((~![T: $i] : (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T)))) | (class_Orderings_Oorder(t_b) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)))),
% 1.00/0.87 inference(quant_inst,[status(thm)],[])).
% 1.00/0.87 tff(57,plain,
% 1.00/0.87 ((~![T: $i] : (class_Orderings_Oorder(T) | (~class_OrderedGroup_Olordered__ab__group__abs(T)))) | class_Orderings_Oorder(t_b) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[56, 55])).
% 1.00/0.87 tff(58,plain,
% 1.00/0.87 (class_Orderings_Oorder(t_b)),
% 1.00/0.87 inference(unit_resolution,[status(thm)],[57, 54, 44])).
% 1.00/0.87 tff(59,plain,
% 1.00/0.87 (^[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))))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(60,plain,
% 1.00/0.87 (![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))) <=> ![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)))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[59])).
% 1.00/0.87 tff(61,plain,
% 1.00/0.87 (![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))) <=> ![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)))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(62,plain,
% 1.00/0.87 (^[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)))))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(63,plain,
% 1.00/0.87 (![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)))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[62])).
% 1.00/0.87 tff(64,axiom,(![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((((~class_Orderings_Oorder(T_a)) | (~c_lessequals(V_y, V_z, T_a))) | (~c_lessequals(V_x, V_y, T_a))) | c_lessequals(V_x, V_z, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Orderings_Oorder__class_Oorder__trans_0')).
% 1.00/0.87 tff(65,plain,
% 1.00/0.87 (![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)))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[64, 63])).
% 1.00/0.87 tff(66,plain,
% 1.00/0.87 (![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)))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[65, 61])).
% 1.00/0.87 tff(67,plain,(
% 1.00/0.87 ![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)))),
% 1.00/0.87 inference(skolemize,[status(sab)],[66])).
% 1.00/0.87 tff(68,plain,
% 1.00/0.87 (![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)))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[67, 60])).
% 1.00/0.87 tff(69,plain,
% 1.00/0.87 (((~![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(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) | (~c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), 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_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) | (~c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(70,plain,
% 1.00/0.87 ((c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) | (~c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)) | (~class_Orderings_Oorder(t_b))) <=> ((~class_Orderings_Oorder(t_b)) | c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) | (~c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(71,plain,
% 1.00/0.87 (((~![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(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) | (~c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), 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_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) | (~c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b))))),
% 1.00/0.87 inference(monotonicity,[status(thm)],[70])).
% 1.00/0.87 tff(72,plain,
% 1.00/0.87 (((~![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(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) | (~c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), 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_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) | (~c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)))),
% 1.00/0.87 inference(transitivity,[status(thm)],[71, 69])).
% 1.00/0.87 tff(73,plain,
% 1.00/0.87 ((~![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(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) | (~c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)) | (~class_Orderings_Oorder(t_b)))),
% 1.00/0.87 inference(quant_inst,[status(thm)],[])).
% 1.00/0.87 tff(74,plain,
% 1.00/0.87 ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_x, V_y, T_a)) | (~c_lessequals(V_y, V_z, T_a)) | (~class_Orderings_Oorder(T_a)))) | (~class_Orderings_Oorder(t_b)) | c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) | (~c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.00/0.87 tff(75,plain,
% 1.00/0.87 ($false),
% 1.00/0.87 inference(unit_resolution,[status(thm)],[74, 68, 58, 33, 24, 15])).
% 1.00/0.87 tff(76,plain,(c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)), inference(lemma,lemma(discharge,[]))).
% 1.00/0.87 tff(77,plain,
% 1.00/0.87 (^[T_a: $i, V_y: $i] : refl(((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a))) <=> ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a))))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(78,plain,
% 1.00/0.87 (![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a))) <=> ![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[77])).
% 1.00/0.87 tff(79,plain,
% 1.00/0.87 (![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a))) <=> ![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(80,plain,
% 1.00/0.87 (^[T_a: $i, V_y: $i] : rewrite((((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (~c_lessequals(c_0, V_y, T_a))) | (c_HOL_Oabs(V_y, T_a) = V_y)) <=> ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a))))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(81,plain,
% 1.00/0.87 (![T_a: $i, V_y: $i] : (((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (~c_lessequals(c_0, V_y, T_a))) | (c_HOL_Oabs(V_y, T_a) = V_y)) <=> ![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[80])).
% 1.00/0.87 tff(82,axiom,(![T_a: $i, V_y: $i] : (((~class_OrderedGroup_Olordered__ab__group__abs(T_a)) | (~c_lessequals(c_0, V_y, T_a))) | (c_HOL_Oabs(V_y, T_a) = V_y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OrderedGroup_Oabs__of__nonneg_0')).
% 1.00/0.87 tff(83,plain,
% 1.00/0.87 (![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.00/0.87 tff(84,plain,
% 1.00/0.87 (![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[83, 79])).
% 1.00/0.87 tff(85,plain,(
% 1.00/0.87 ![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))),
% 1.00/0.87 inference(skolemize,[status(sab)],[84])).
% 1.00/0.87 tff(86,plain,
% 1.00/0.87 (![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[85, 78])).
% 1.00/0.87 tff(87,plain,
% 1.00/0.87 (((~![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (~c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)) | (c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)))) <=> ((~![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (~c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)) | (c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(88,plain,
% 1.00/0.87 (((c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b))) <=> ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (~c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)) | (c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(89,plain,
% 1.00/0.87 (((~![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))) | ((c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)))) <=> ((~![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))) | ((~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (~c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)) | (c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b))))),
% 1.00/0.87 inference(monotonicity,[status(thm)],[88])).
% 1.00/0.87 tff(90,plain,
% 1.00/0.87 (((~![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))) | ((c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)))) <=> ((~![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (~c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)) | (c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)))),
% 1.00/0.87 inference(transitivity,[status(thm)],[89, 87])).
% 1.00/0.87 tff(91,plain,
% 1.00/0.87 ((~![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))) | ((c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)) | (~c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)))),
% 1.00/0.87 inference(quant_inst,[status(thm)],[])).
% 1.00/0.87 tff(92,plain,
% 1.00/0.87 ((~![T_a: $i, V_y: $i] : ((c_HOL_Oabs(V_y, T_a) = V_y) | (~c_lessequals(c_0, V_y, T_a)) | (~class_OrderedGroup_Olordered__ab__group__abs(T_a)))) | (~class_OrderedGroup_Olordered__ab__group__abs(t_b)) | (~c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)) | (c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.00/0.87 tff(93,plain,
% 1.00/0.87 ((~c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)) | (c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b))),
% 1.00/0.87 inference(unit_resolution,[status(thm)],[92, 86, 44])).
% 1.00/0.87 tff(94,plain,
% 1.00/0.87 (c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) = c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)),
% 1.00/0.87 inference(unit_resolution,[status(thm)],[93, 76])).
% 1.00/0.87 tff(95,plain,
% 1.00/0.87 (c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b) = c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)),
% 1.00/0.87 inference(symmetry,[status(thm)],[94])).
% 1.00/0.87 tff(96,plain,
% 1.00/0.87 (c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b) = c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)),
% 1.00/0.87 inference(transitivity,[status(thm)],[95, 14])).
% 1.00/0.87 tff(97,plain,
% 1.00/0.87 (c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b) <=> c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), t_b)),
% 1.00/0.87 inference(monotonicity,[status(thm)],[96])).
% 1.00/0.87 tff(98,plain,
% 1.00/0.87 (c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), t_b) <=> c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)),
% 1.00/0.87 inference(symmetry,[status(thm)],[97])).
% 1.00/0.87 tff(99,plain,
% 1.00/0.87 ((~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), t_b)) <=> (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b))),
% 1.00/0.87 inference(monotonicity,[status(thm)],[98])).
% 1.00/0.87 tff(100,plain,
% 1.00/0.87 (^[V_U: $i] : refl((~c_lessequals(v_f(v_x(V_U)), c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b)) <=> (~c_lessequals(v_f(v_x(V_U)), c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b)))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(101,plain,
% 1.00/0.87 (![V_U: $i] : (~c_lessequals(v_f(v_x(V_U)), c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b)) <=> ![V_U: $i] : (~c_lessequals(v_f(v_x(V_U)), c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[100])).
% 1.00/0.87 tff(102,plain,
% 1.00/0.87 (![V_U: $i] : (~c_lessequals(v_f(v_x(V_U)), c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b)) <=> ![V_U: $i] : (~c_lessequals(v_f(v_x(V_U)), c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b))),
% 1.00/0.88 inference(rewrite,[status(thm)],[])).
% 1.00/0.88 tff(103,axiom,(![V_U: $i] : (~c_lessequals(v_f(v_x(V_U)), c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 1.00/0.88 tff(104,plain,
% 1.00/0.88 (![V_U: $i] : (~c_lessequals(v_f(v_x(V_U)), c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b))),
% 1.00/0.88 inference(modus_ponens,[status(thm)],[103, 102])).
% 1.00/0.88 tff(105,plain,(
% 1.00/0.88 ![V_U: $i] : (~c_lessequals(v_f(v_x(V_U)), c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b))),
% 1.00/0.88 inference(skolemize,[status(sab)],[104])).
% 1.00/0.88 tff(106,plain,
% 1.00/0.88 (![V_U: $i] : (~c_lessequals(v_f(v_x(V_U)), c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b))),
% 1.00/0.88 inference(modus_ponens,[status(thm)],[105, 101])).
% 1.00/0.88 tff(107,plain,
% 1.00/0.88 ((~![V_U: $i] : (~c_lessequals(v_f(v_x(V_U)), c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b))) | (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), t_b))),
% 1.00/0.88 inference(quant_inst,[status(thm)],[])).
% 1.00/0.88 tff(108,plain,
% 1.00/0.88 (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), t_b)),
% 1.00/0.88 inference(unit_resolution,[status(thm)],[107, 106])).
% 1.00/0.88 tff(109,plain,
% 1.00/0.88 (~c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)),
% 1.00/0.88 inference(modus_ponens,[status(thm)],[108, 99])).
% 1.00/0.88 tff(110,plain,
% 1.00/0.88 ($false),
% 1.00/0.88 inference(unit_resolution,[status(thm)],[24, 109])).
% 1.00/0.88 % SZS output end Proof
%------------------------------------------------------------------------------