%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA015-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 09:30:36 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.26s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA015-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n004.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 20:28:37 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.26 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.09/0.26
% 0.09/0.26 % SZS status Unsatisfiable
% 0.09/0.26
% 0.22/0.27 % SZS output start Proof
% 0.22/0.27 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__field(t_a) = true.
% 0.22/0.27 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.22/0.27 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.22/0.27 Axiom 4 (clsrel_Ring__and__Field_Oordered__field_47): ifeq(class_Ring__and__Field_Oordered__field(X), true, class_OrderedGroup_Olordered__ab__group__abs(X), true) = true.
% 0.22/0.27 Axiom 5 (clsrel_Ring__and__Field_Oordered__field_34): ifeq(class_Ring__and__Field_Oordered__field(X), true, class_Ring__and__Field_Oordered__idom(X), true) = true.
% 0.22/0.27 Axiom 6 (clsrel_Ring__and__Field_Oordered__field_46): ifeq(class_Ring__and__Field_Oordered__field(X), true, class_Ring__and__Field_Opordered__semiring(X), true) = true.
% 0.22/0.27 Axiom 7 (clsrel_Ring__and__Field_Oordered__field_0): ifeq(class_Ring__and__Field_Oordered__field(X), true, class_Ring__and__Field_Ofield(X), true) = true.
% 0.22/0.27 Axiom 8 (clsrel_Ring__and__Field_Ofield_21): ifeq(class_Ring__and__Field_Ofield(X), true, class_OrderedGroup_Osemigroup__mult(X), true) = true.
% 0.22/0.27 Axiom 9 (cls_OrderedGroup_Oabs__ge__zero_0): ifeq(class_OrderedGroup_Olordered__ab__group__abs(X), true, c_lessequals(c_0, c_HOL_Oabs(Y, X), X), true) = true.
% 0.22/0.27 Axiom 10 (cls_conjecture_1): c_lessequals(c_HOL_Oabs(v_g(X), t_a), c_times(v_d, c_HOL_Oabs(v_f(X), t_a), t_a), t_a) = true.
% 0.22/0.27 Axiom 11 (cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0): ifeq2(class_OrderedGroup_Osemigroup__mult(X), true, c_times(c_times(Y, Z, X), W, X), c_times(Y, c_times(Z, W, X), X)) = c_times(Y, c_times(Z, W, X), X).
% 0.22/0.27 Axiom 12 (cls_Ring__and__Field_Oabs__mult_0): ifeq2(class_Ring__and__Field_Oordered__idom(X), true, c_times(c_HOL_Oabs(Y, X), c_HOL_Oabs(Z, X), X), c_HOL_Oabs(c_times(Y, Z, X), X)) = c_HOL_Oabs(c_times(Y, Z, X), X).
% 0.22/0.27 Axiom 13 (cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0): ifeq(class_Ring__and__Field_Opordered__semiring(X), true, ifeq(c_lessequals(c_0, Y, X), true, ifeq(c_lessequals(Z, W, X), true, c_lessequals(c_times(Y, Z, X), c_times(Y, W, X), X), true), true), true) = true.
% 0.22/0.27
% 0.22/0.27 Goal 1 (cls_conjecture_2): c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(X)), t_a), t_a), c_times(X, c_HOL_Oabs(v_f(v_x(X)), t_a), t_a), t_a) = true.
% 0.22/0.27 The goal is true when:
% 0.22/0.27 X = c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a)
% 0.22/0.27
% 0.22/0.27 Proof:
% 0.22/0.27 c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a), c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a)
% 0.22/0.27 = { by axiom 3 (ifeq_axiom) R->L }
% 0.22/0.27 c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), ifeq2(true, true, c_times(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a), c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a)), t_a)
% 0.22/0.27 = { by axiom 8 (clsrel_Ring__and__Field_Ofield_21) R->L }
% 0.22/0.27 c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), ifeq2(ifeq(class_Ring__and__Field_Ofield(t_a), true, class_OrderedGroup_Osemigroup__mult(t_a), true), true, c_times(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a), c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a)), t_a)
% 0.22/0.27 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.27 c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), ifeq2(ifeq(ifeq(true, true, class_Ring__and__Field_Ofield(t_a), true), true, class_OrderedGroup_Osemigroup__mult(t_a), true), true, c_times(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a), c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a)), t_a)
% 0.22/0.27 = { by axiom 1 (tfree_tcs) R->L }
% 0.22/0.27 c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), ifeq2(ifeq(ifeq(class_Ring__and__Field_Oordered__field(t_a), true, class_Ring__and__Field_Ofield(t_a), true), true, class_OrderedGroup_Osemigroup__mult(t_a), true), true, c_times(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a), c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a)), t_a)
% 0.22/0.27 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__field_0) }
% 0.22/0.27 c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), ifeq2(ifeq(true, true, class_OrderedGroup_Osemigroup__mult(t_a), true), true, c_times(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a), c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a)), t_a)
% 0.22/0.27 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.27 c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), ifeq2(class_OrderedGroup_Osemigroup__mult(t_a), true, c_times(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a), c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a)), t_a)
% 0.22/0.27 = { by axiom 11 (cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) }
% 0.22/0.27 c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a)
% 0.22/0.27 = { by axiom 12 (cls_Ring__and__Field_Oabs__mult_0) R->L }
% 0.22/0.27 c_lessequals(ifeq2(class_Ring__and__Field_Oordered__idom(t_a), true, c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a)), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a)
% 0.22/0.27 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.27 c_lessequals(ifeq2(ifeq(true, true, class_Ring__and__Field_Oordered__idom(t_a), true), true, c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a)), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a)
% 0.22/0.27 = { by axiom 1 (tfree_tcs) R->L }
% 0.22/0.27 c_lessequals(ifeq2(ifeq(class_Ring__and__Field_Oordered__field(t_a), true, class_Ring__and__Field_Oordered__idom(t_a), true), true, c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a)), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a)
% 0.22/0.27 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__field_34) }
% 0.22/0.27 c_lessequals(ifeq2(true, true, c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c, t_a), v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a)), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a)
% 0.22/0.27 = { by axiom 3 (ifeq_axiom) }
% 0.22/0.27 c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a)
% 0.22/0.27 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.27 ifeq(true, true, c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a), true)
% 0.22/0.27 = { by axiom 10 (cls_conjecture_1) R->L }
% 0.22/0.27 ifeq(c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), true, c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a), true)
% 0.22/0.27 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.27 ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), true, c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a), true), true)
% 0.22/0.27 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.27 ifeq(true, true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), true, c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a), true), true), true)
% 0.22/0.27 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__field_46) R->L }
% 0.22/0.27 ifeq(ifeq(class_Ring__and__Field_Oordered__field(t_a), true, class_Ring__and__Field_Opordered__semiring(t_a), true), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), true, c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a), true), true), true)
% 0.22/0.27 = { by axiom 1 (tfree_tcs) }
% 0.22/0.27 ifeq(ifeq(true, true, class_Ring__and__Field_Opordered__semiring(t_a), true), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), true, c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a), true), true), true)
% 0.22/0.27 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.27 ifeq(class_Ring__and__Field_Opordered__semiring(t_a), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), true, c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a), true), true), true)
% 0.22/0.28 = { by axiom 9 (cls_OrderedGroup_Oabs__ge__zero_0) R->L }
% 0.22/0.28 ifeq(class_Ring__and__Field_Opordered__semiring(t_a), true, ifeq(ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_a), true, c_lessequals(c_0, c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), t_a), true), true, ifeq(c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), true, c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a), true), true), true)
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.28 ifeq(class_Ring__and__Field_Opordered__semiring(t_a), true, ifeq(ifeq(ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_a), true), true, c_lessequals(c_0, c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), t_a), true), true, ifeq(c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), true, c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a), true), true), true)
% 0.22/0.28 = { by axiom 1 (tfree_tcs) R->L }
% 0.22/0.28 ifeq(class_Ring__and__Field_Opordered__semiring(t_a), true, ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__field(t_a), true, class_OrderedGroup_Olordered__ab__group__abs(t_a), true), true, c_lessequals(c_0, c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), t_a), true), true, ifeq(c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), true, c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a), true), true), true)
% 0.22/0.28 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__field_47) }
% 0.22/0.28 ifeq(class_Ring__and__Field_Opordered__semiring(t_a), true, ifeq(ifeq(true, true, c_lessequals(c_0, c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), t_a), true), true, ifeq(c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), true, c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a), true), true), true)
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.28 ifeq(class_Ring__and__Field_Opordered__semiring(t_a), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), t_a), true, ifeq(c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), true, c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), c_times(v_d, c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c, t_a), t_a), v_d, t_a))), t_a), t_a), t_a), t_a), true), true), true)
% 0.22/0.28 = { by axiom 13 (cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) }
% 0.22/0.28 true
% 0.22/0.28 % SZS output end Proof
% 0.22/0.28
% 0.22/0.28 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------