%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA030-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:30:38 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.27s
% Output : Proof 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA030-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n010.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Mon Sep 28 20:32:32 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.27 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 0.09/0.27
% 0.09/0.27 % SZS status Unsatisfiable
% 0.09/0.27
% 0.09/0.29 % SZS output start Proof
% 0.09/0.29 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.09/0.29 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.09/0.29 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.09/0.29 Axiom 4 (clsrel_Ring__and__Field_Oordered__idom_4): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Oab__group__add(X), true) = true.
% 0.09/0.29 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_50): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Olordered__ab__group__abs(X), true) = true.
% 0.09/0.29 Axiom 6 (clsrel_Ring__and__Field_Oordered__idom_33): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_Orderings_Olinorder(X), true) = true.
% 0.09/0.29 Axiom 7 (clsrel_OrderedGroup_Olordered__ab__group__abs_1): ifeq(class_OrderedGroup_Olordered__ab__group__abs(X), true, class_OrderedGroup_Opordered__ab__group__add(X), true) = true.
% 0.09/0.29 Axiom 8 (cls_OrderedGroup_Ominus__minus_0): ifeq2(class_OrderedGroup_Oab__group__add(X), true, c_uminus(c_uminus(Y, X), X), Y) = Y.
% 0.09/0.29 Axiom 9 (cls_Orderings_Ole__maxI2_0): ifeq(class_Orderings_Olinorder(X), true, c_lessequals(Y, c_Orderings_Omax(Z, Y, X), X), true) = true.
% 0.09/0.29 Axiom 10 (cls_OrderedGroup_Ominus__diff__eq_0): ifeq2(class_OrderedGroup_Oab__group__add(X), true, c_uminus(c_minus(Y, Z, X), X), c_minus(Z, Y, X)) = c_minus(Z, Y, X).
% 0.09/0.29 Axiom 11 (cls_OrderedGroup_Odiff__minus__eq__add_0): ifeq2(class_OrderedGroup_Oab__group__add(X), true, c_minus(Y, c_uminus(Z, X), X), c_plus(Y, Z, X)) = c_plus(Y, Z, X).
% 0.09/0.29 Axiom 12 (cls_OrderedGroup_Ocompare__rls__1_0): ifeq2(class_OrderedGroup_Oab__group__add(X), true, c_plus(Y, c_uminus(Z, X), X), c_minus(Y, Z, X)) = c_minus(Y, Z, X).
% 0.09/0.30 Axiom 13 (cls_OrderedGroup_Oabs__of__nonneg_0): ifeq2(class_OrderedGroup_Olordered__ab__group__abs(X), true, ifeq2(c_lessequals(c_0, Y, X), true, c_HOL_Oabs(Y, X), Y), Y) = Y.
% 0.09/0.30 Axiom 14 (cls_OrderedGroup_Ominus__add__distrib_0): ifeq2(class_OrderedGroup_Oab__group__add(X), true, c_plus(c_uminus(Y, X), c_uminus(Z, X), X), c_uminus(c_plus(Y, Z, X), X)) = c_uminus(c_plus(Y, Z, X), X).
% 0.09/0.30 Axiom 15 (cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0): ifeq(class_Orderings_Olinorder(X), true, ifeq(c_lessequals(c_Orderings_Omax(Y, Z, X), W, X), true, c_lessequals(Y, W, X), true), true) = true.
% 0.09/0.30 Axiom 16 (cls_conjecture_1): c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(X), v_g(X), t_b), c_0, t_b), t_b), c_times(v_c, c_HOL_Oabs(v_h(X), t_b), t_b), t_b) = true.
% 0.09/0.30 Axiom 17 (cls_OrderedGroup_Ocompare__rls__8_0): ifeq(class_OrderedGroup_Opordered__ab__group__add(X), true, ifeq(c_lessequals(c_minus(Y, Z, X), W, X), true, c_lessequals(Y, c_plus(W, Z, X), X), true), true) = true.
% 0.09/0.30
% 0.09/0.30 Lemma 18: c_minus(X, c_uminus(Y, t_b), t_b) = c_plus(X, Y, t_b).
% 0.09/0.30 Proof:
% 0.09/0.30 c_minus(X, c_uminus(Y, t_b), t_b)
% 0.09/0.30 = { by axiom 3 (ifeq_axiom) R->L }
% 0.09/0.30 ifeq2(true, true, c_minus(X, c_uminus(Y, t_b), t_b), c_plus(X, Y, t_b))
% 0.09/0.30 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 0.09/0.30 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_minus(X, c_uminus(Y, t_b), t_b), c_plus(X, Y, t_b))
% 0.09/0.30 = { by axiom 1 (tfree_tcs) }
% 0.09/0.30 ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_minus(X, c_uminus(Y, t_b), t_b), c_plus(X, Y, t_b))
% 0.09/0.30 = { by axiom 2 (ifeq_axiom) }
% 0.09/0.30 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_minus(X, c_uminus(Y, t_b), t_b), c_plus(X, Y, t_b))
% 0.09/0.30 = { by axiom 11 (cls_OrderedGroup_Odiff__minus__eq__add_0) }
% 0.09/0.30 c_plus(X, Y, t_b)
% 0.09/0.30
% 0.09/0.30 Lemma 19: c_plus(X, c_uminus(Y, t_b), t_b) = c_minus(X, Y, t_b).
% 0.09/0.30 Proof:
% 0.09/0.30 c_plus(X, c_uminus(Y, t_b), t_b)
% 0.09/0.30 = { by axiom 3 (ifeq_axiom) R->L }
% 0.09/0.30 ifeq2(true, true, c_plus(X, c_uminus(Y, t_b), t_b), c_minus(X, Y, t_b))
% 0.09/0.30 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 0.09/0.30 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(X, c_uminus(Y, t_b), t_b), c_minus(X, Y, t_b))
% 0.09/0.30 = { by axiom 1 (tfree_tcs) }
% 0.09/0.30 ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(X, c_uminus(Y, t_b), t_b), c_minus(X, Y, t_b))
% 0.09/0.30 = { by axiom 2 (ifeq_axiom) }
% 0.09/0.30 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(X, c_uminus(Y, t_b), t_b), c_minus(X, Y, t_b))
% 0.09/0.30 = { by axiom 12 (cls_OrderedGroup_Ocompare__rls__1_0) }
% 0.09/0.30 c_minus(X, Y, t_b)
% 0.09/0.30
% 0.09/0.30 Goal 1 (cls_conjecture_2): c_lessequals(v_f(v_x(X)), c_plus(v_g(v_x(X)), c_times(X, c_HOL_Oabs(v_h(v_x(X)), t_b), t_b), t_b), t_b) = true.
% 0.09/0.30 The goal is true when:
% 0.09/0.30 X = v_c
% 0.09/0.30
% 0.09/0.30 Proof:
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), c_plus(v_g(v_x(v_c)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b)
% 0.09/0.30 = { by axiom 8 (cls_OrderedGroup_Ominus__minus_0) R->L }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), c_plus(ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_uminus(c_uminus(v_g(v_x(v_c)), t_b), t_b), v_g(v_x(v_c))), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b)
% 0.09/0.30 = { by axiom 2 (ifeq_axiom) R->L }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), c_plus(ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_uminus(c_uminus(v_g(v_x(v_c)), t_b), t_b), v_g(v_x(v_c))), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b)
% 0.09/0.30 = { by axiom 1 (tfree_tcs) R->L }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), c_plus(ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_uminus(c_uminus(v_g(v_x(v_c)), t_b), t_b), v_g(v_x(v_c))), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b)
% 0.09/0.30 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_4) }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), c_plus(ifeq2(true, true, c_uminus(c_uminus(v_g(v_x(v_c)), t_b), t_b), v_g(v_x(v_c))), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b)
% 0.09/0.30 = { by axiom 3 (ifeq_axiom) }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), c_plus(c_uminus(c_uminus(v_g(v_x(v_c)), t_b), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b)
% 0.09/0.30 = { by lemma 18 R->L }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), c_minus(c_uminus(c_uminus(v_g(v_x(v_c)), t_b), t_b), c_uminus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), t_b)
% 0.09/0.30 = { by lemma 19 R->L }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), c_plus(c_uminus(c_uminus(v_g(v_x(v_c)), t_b), t_b), c_uminus(c_uminus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), t_b), t_b)
% 0.09/0.30 = { by axiom 3 (ifeq_axiom) R->L }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), ifeq2(true, true, c_plus(c_uminus(c_uminus(v_g(v_x(v_c)), t_b), t_b), c_uminus(c_uminus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), t_b), c_uminus(c_minus(c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b)), t_b)
% 0.09/0.30 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_uminus(c_uminus(v_g(v_x(v_c)), t_b), t_b), c_uminus(c_uminus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), t_b), c_uminus(c_minus(c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b)), t_b)
% 0.09/0.30 = { by axiom 1 (tfree_tcs) }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_uminus(c_uminus(v_g(v_x(v_c)), t_b), t_b), c_uminus(c_uminus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), t_b), c_uminus(c_minus(c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b)), t_b)
% 0.09/0.30 = { by axiom 2 (ifeq_axiom) }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_uminus(c_uminus(v_g(v_x(v_c)), t_b), t_b), c_uminus(c_uminus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), t_b), c_uminus(c_minus(c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b)), t_b)
% 0.09/0.30 = { by lemma 19 R->L }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_uminus(c_uminus(v_g(v_x(v_c)), t_b), t_b), c_uminus(c_uminus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), t_b), c_uminus(c_plus(c_uminus(v_g(v_x(v_c)), t_b), c_uminus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), t_b)), t_b)
% 0.09/0.30 = { by axiom 14 (cls_OrderedGroup_Ominus__add__distrib_0) }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), c_uminus(c_plus(c_uminus(v_g(v_x(v_c)), t_b), c_uminus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), t_b), t_b)
% 0.09/0.30 = { by lemma 19 }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), c_uminus(c_minus(c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), t_b)
% 0.09/0.30 = { by axiom 3 (ifeq_axiom) R->L }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), ifeq2(true, true, c_uminus(c_minus(c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), c_minus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), c_uminus(v_g(v_x(v_c)), t_b), t_b)), t_b)
% 0.09/0.30 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 0.09/0.30 c_lessequals(v_f(v_x(v_c)), ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_uminus(c_minus(c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), c_minus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), c_uminus(v_g(v_x(v_c)), t_b), t_b)), t_b)
% 0.65/0.30 = { by axiom 1 (tfree_tcs) }
% 0.65/0.30 c_lessequals(v_f(v_x(v_c)), ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_uminus(c_minus(c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), c_minus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), c_uminus(v_g(v_x(v_c)), t_b), t_b)), t_b)
% 0.65/0.30 = { by axiom 2 (ifeq_axiom) }
% 0.65/0.30 c_lessequals(v_f(v_x(v_c)), ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_uminus(c_minus(c_uminus(v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), t_b), c_minus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), c_uminus(v_g(v_x(v_c)), t_b), t_b)), t_b)
% 0.65/0.30 = { by axiom 10 (cls_OrderedGroup_Ominus__diff__eq_0) }
% 0.65/0.30 c_lessequals(v_f(v_x(v_c)), c_minus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), c_uminus(v_g(v_x(v_c)), t_b), t_b), t_b)
% 0.65/0.30 = { by lemma 18 }
% 0.65/0.30 c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b)
% 0.65/0.30 = { by axiom 2 (ifeq_axiom) R->L }
% 0.65/0.30 ifeq(true, true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true)
% 0.65/0.30 = { by axiom 2 (ifeq_axiom) R->L }
% 0.65/0.30 ifeq(true, true, ifeq(true, true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.30 = { by axiom 7 (clsrel_OrderedGroup_Olordered__ab__group__abs_1) R->L }
% 0.65/0.30 ifeq(ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, ifeq(true, true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.30 = { by axiom 2 (ifeq_axiom) R->L }
% 0.65/0.30 ifeq(ifeq(ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, ifeq(true, true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.30 = { by axiom 1 (tfree_tcs) R->L }
% 0.65/0.30 ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, ifeq(true, true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.30 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 0.65/0.30 ifeq(ifeq(true, true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, ifeq(true, true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.30 = { by axiom 2 (ifeq_axiom) }
% 0.65/0.30 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(true, true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.30 = { by axiom 15 (cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) R->L }
% 0.65/0.30 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(class_Orderings_Olinorder(t_b), true, ifeq(c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.30 = { by axiom 13 (cls_OrderedGroup_Oabs__of__nonneg_0) R->L }
% 0.65/0.30 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(class_Orderings_Olinorder(t_b), true, ifeq(c_lessequals(ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, ifeq2(c_lessequals(c_0, c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), true, c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.30 = { by axiom 2 (ifeq_axiom) R->L }
% 0.65/0.30 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(class_Orderings_Olinorder(t_b), true, ifeq(c_lessequals(ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, ifeq2(ifeq(true, true, c_lessequals(c_0, c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), true), true, c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.30 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_33) R->L }
% 0.65/0.30 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(class_Orderings_Olinorder(t_b), true, ifeq(c_lessequals(ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, ifeq2(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_Orderings_Olinorder(t_b), true), true, c_lessequals(c_0, c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), true), true, c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.30 = { by axiom 1 (tfree_tcs) }
% 0.65/0.30 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(class_Orderings_Olinorder(t_b), true, ifeq(c_lessequals(ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, ifeq2(ifeq(ifeq(true, true, class_Orderings_Olinorder(t_b), true), true, c_lessequals(c_0, c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), true), true, c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.30 = { by axiom 2 (ifeq_axiom) }
% 0.65/0.31 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(class_Orderings_Olinorder(t_b), true, ifeq(c_lessequals(ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, ifeq2(ifeq(class_Orderings_Olinorder(t_b), true, c_lessequals(c_0, c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), true), true, c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.31 = { by axiom 9 (cls_Orderings_Ole__maxI2_0) }
% 0.65/0.31 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(class_Orderings_Olinorder(t_b), true, ifeq(c_lessequals(ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, ifeq2(true, true, c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.31 = { by axiom 2 (ifeq_axiom) R->L }
% 0.65/0.31 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(class_Orderings_Olinorder(t_b), true, ifeq(c_lessequals(ifeq2(ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, ifeq2(true, true, c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.31 = { by axiom 1 (tfree_tcs) R->L }
% 0.65/0.31 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(class_Orderings_Olinorder(t_b), true, ifeq(c_lessequals(ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, ifeq2(true, true, c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.31 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 0.65/0.31 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(class_Orderings_Olinorder(t_b), true, ifeq(c_lessequals(ifeq2(true, true, ifeq2(true, true, c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.31 = { by axiom 3 (ifeq_axiom) }
% 0.65/0.31 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(class_Orderings_Olinorder(t_b), true, ifeq(c_lessequals(ifeq2(true, true, c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b)), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.31 = { by axiom 3 (ifeq_axiom) }
% 0.65/0.31 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(class_Orderings_Olinorder(t_b), true, ifeq(c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_0, t_b), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.31 = { by axiom 16 (cls_conjecture_1) }
% 0.65/0.31 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(class_Orderings_Olinorder(t_b), true, ifeq(true, true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.31 = { by axiom 2 (ifeq_axiom) R->L }
% 0.65/0.31 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(ifeq(true, true, class_Orderings_Olinorder(t_b), true), true, ifeq(true, true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.31 = { by axiom 1 (tfree_tcs) R->L }
% 0.65/0.31 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_Orderings_Olinorder(t_b), true), true, ifeq(true, true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.31 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_33) }
% 0.65/0.31 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(true, true, ifeq(true, true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.31 = { by axiom 2 (ifeq_axiom) }
% 0.65/0.31 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(ifeq(true, true, c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.31 = { by axiom 2 (ifeq_axiom) }
% 0.65/0.31 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(c_lessequals(c_minus(v_f(v_x(v_c)), v_g(v_x(v_c)), t_b), c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), t_b), true, c_lessequals(v_f(v_x(v_c)), c_plus(c_times(v_c, c_HOL_Oabs(v_h(v_x(v_c)), t_b), t_b), v_g(v_x(v_c)), t_b), t_b), true), true)
% 0.65/0.31 = { by axiom 17 (cls_OrderedGroup_Ocompare__rls__8_0) }
% 0.65/0.31 true
% 0.65/0.31 % SZS output end Proof
% 0.65/0.31
% 0.65/0.31 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------