%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA028-2 : 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 0.21s 0.37s
% Output : Proof 1.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA028-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n010.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 20:32:20 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.37 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
% 0.21/0.37
% 0.21/0.37 % SZS status Unsatisfiable
% 0.21/0.37
% 1.40/0.42 % SZS output start Proof
% 1.40/0.42 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 1.40/0.42 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.40/0.42 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 1.40/0.42 Axiom 4 (cls_conjecture_1): c_lessequals(v_g(X), v_k(X), t_b) = true.
% 1.40/0.43 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_4): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Oab__group__add(X), true) = true.
% 1.40/0.43 Axiom 6 (clsrel_Ring__and__Field_Oordered__idom_54): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Opordered__ab__group__add(X), true) = true.
% 1.40/0.43 Axiom 7 (clsrel_Ring__and__Field_Oordered__idom_23): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Ocomm__monoid__add(X), true) = true.
% 1.40/0.43 Axiom 8 (cls_OrderedGroup_Odiff__self_0): ifeq2(class_OrderedGroup_Oab__group__add(X), true, c_minus(Y, Y, X), c_0) = c_0.
% 1.40/0.43 Axiom 9 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0): ifeq2(class_OrderedGroup_Ocomm__monoid__add(X), true, c_plus(c_0, Y, X), Y) = Y.
% 1.40/0.43 Axiom 10 (cls_OrderedGroup_Ocompare__rls__5_0): ifeq2(class_OrderedGroup_Oab__group__add(X), true, c_minus(Y, c_minus(Z, W, X), X), c_minus(c_plus(Y, W, X), Z, X)) = c_minus(c_plus(Y, W, X), Z, X).
% 1.40/0.43 Axiom 11 (cls_OrderedGroup_Ocompare__rls__2_0): ifeq2(class_OrderedGroup_Oab__group__add(X), true, c_plus(Y, c_minus(Z, W, X), X), c_minus(c_plus(Y, Z, X), W, X)) = c_minus(c_plus(Y, Z, X), W, X).
% 1.40/0.43 Axiom 12 (cls_OrderedGroup_Ocompare__rls__3_0): ifeq2(class_OrderedGroup_Oab__group__add(X), true, c_plus(c_minus(Y, Z, X), W, X), c_minus(c_plus(Y, W, X), Z, X)) = c_minus(c_plus(Y, W, X), Z, X).
% 1.40/0.43 Axiom 13 (cls_OrderedGroup_Ocompare__rls__8_1): ifeq(c_lessequals(X, c_plus(Y, Z, W), W), true, ifeq(class_OrderedGroup_Opordered__ab__group__add(W), true, c_lessequals(c_minus(X, Z, W), Y, W), true), true) = true.
% 1.40/0.43
% 1.40/0.43 Lemma 14: c_plus(c_0, X, t_b) = X.
% 1.40/0.43 Proof:
% 1.40/0.43 c_plus(c_0, X, t_b)
% 1.40/0.43 = { by axiom 3 (ifeq_axiom) R->L }
% 1.40/0.43 ifeq2(true, true, c_plus(c_0, X, t_b), X)
% 1.40/0.43 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_23) R->L }
% 1.40/0.43 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Ocomm__monoid__add(t_b), true), true, c_plus(c_0, X, t_b), X)
% 1.40/0.43 = { by axiom 1 (tfree_tcs) }
% 1.40/0.43 ifeq2(ifeq(true, true, class_OrderedGroup_Ocomm__monoid__add(t_b), true), true, c_plus(c_0, X, t_b), X)
% 1.40/0.43 = { by axiom 2 (ifeq_axiom) }
% 1.40/0.43 ifeq2(class_OrderedGroup_Ocomm__monoid__add(t_b), true, c_plus(c_0, X, t_b), X)
% 1.40/0.43 = { by axiom 9 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) }
% 1.40/0.43 X
% 1.40/0.43
% 1.40/0.43 Lemma 15: c_minus(X, X, t_b) = c_0.
% 1.40/0.43 Proof:
% 1.40/0.43 c_minus(X, X, t_b)
% 1.40/0.43 = { by axiom 3 (ifeq_axiom) R->L }
% 1.40/0.43 ifeq2(true, true, c_minus(X, X, t_b), c_0)
% 1.40/0.43 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 1.40/0.43 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_minus(X, X, t_b), c_0)
% 1.40/0.43 = { by axiom 1 (tfree_tcs) }
% 1.40/0.43 ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_minus(X, X, t_b), c_0)
% 1.40/0.43 = { by axiom 2 (ifeq_axiom) }
% 1.40/0.43 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_minus(X, X, t_b), c_0)
% 1.40/0.43 = { by axiom 8 (cls_OrderedGroup_Odiff__self_0) }
% 1.40/0.43 c_0
% 1.40/0.43
% 1.40/0.43 Lemma 16: c_minus(c_plus(X, Y, t_b), Z, t_b) = c_minus(X, c_minus(Z, Y, t_b), t_b).
% 1.40/0.43 Proof:
% 1.40/0.43 c_minus(c_plus(X, Y, t_b), Z, t_b)
% 1.40/0.43 = { by axiom 10 (cls_OrderedGroup_Ocompare__rls__5_0) R->L }
% 1.40/0.43 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_minus(X, c_minus(Z, Y, t_b), t_b), c_minus(c_plus(X, Y, t_b), Z, t_b))
% 1.40/0.43 = { by axiom 2 (ifeq_axiom) R->L }
% 1.40/0.43 ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_minus(X, c_minus(Z, Y, t_b), t_b), c_minus(c_plus(X, Y, t_b), Z, t_b))
% 1.40/0.43 = { by axiom 1 (tfree_tcs) R->L }
% 1.40/0.43 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_minus(X, c_minus(Z, Y, t_b), t_b), c_minus(c_plus(X, Y, t_b), Z, t_b))
% 1.40/0.43 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_4) }
% 1.40/0.43 ifeq2(true, true, c_minus(X, c_minus(Z, Y, t_b), t_b), c_minus(c_plus(X, Y, t_b), Z, t_b))
% 1.40/0.43 = { by axiom 3 (ifeq_axiom) }
% 1.40/0.43 c_minus(X, c_minus(Z, Y, t_b), t_b)
% 1.40/0.43
% 1.40/0.43 Lemma 17: c_plus(c_minus(X, Y, t_b), Z, t_b) = c_minus(X, c_minus(Y, Z, t_b), t_b).
% 1.40/0.43 Proof:
% 1.40/0.43 c_plus(c_minus(X, Y, t_b), Z, t_b)
% 1.40/0.43 = { by axiom 3 (ifeq_axiom) R->L }
% 1.40/0.43 ifeq2(true, true, c_plus(c_minus(X, Y, t_b), Z, t_b), c_minus(c_plus(X, Z, t_b), Y, t_b))
% 1.40/0.43 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 1.40/0.43 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_minus(X, Y, t_b), Z, t_b), c_minus(c_plus(X, Z, t_b), Y, t_b))
% 1.40/0.43 = { by axiom 1 (tfree_tcs) }
% 1.40/0.43 ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_minus(X, Y, t_b), Z, t_b), c_minus(c_plus(X, Z, t_b), Y, t_b))
% 1.40/0.43 = { by axiom 2 (ifeq_axiom) }
% 1.40/0.43 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_minus(X, Y, t_b), Z, t_b), c_minus(c_plus(X, Z, t_b), Y, t_b))
% 1.40/0.43 = { by axiom 12 (cls_OrderedGroup_Ocompare__rls__3_0) }
% 1.40/0.43 c_minus(c_plus(X, Z, t_b), Y, t_b)
% 1.40/0.43 = { by lemma 16 }
% 1.40/0.43 c_minus(X, c_minus(Y, Z, t_b), t_b)
% 1.40/0.43
% 1.40/0.43 Lemma 18: c_plus(c_minus(c_0, X, t_b), Y, t_b) = c_minus(Y, X, t_b).
% 1.40/0.43 Proof:
% 1.40/0.43 c_plus(c_minus(c_0, X, t_b), Y, t_b)
% 1.40/0.43 = { by axiom 3 (ifeq_axiom) R->L }
% 1.40/0.43 ifeq2(true, true, c_plus(c_minus(c_0, X, t_b), Y, t_b), c_minus(Y, X, t_b))
% 1.40/0.43 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 1.40/0.43 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_minus(c_0, X, t_b), Y, t_b), c_minus(Y, X, t_b))
% 1.40/0.43 = { by axiom 1 (tfree_tcs) }
% 1.40/0.43 ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_minus(c_0, X, t_b), Y, t_b), c_minus(Y, X, t_b))
% 1.40/0.43 = { by axiom 2 (ifeq_axiom) }
% 1.40/0.43 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_minus(c_0, X, t_b), Y, t_b), c_minus(Y, X, t_b))
% 1.40/0.43 = { by lemma 14 R->L }
% 1.40/0.43 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_minus(c_0, X, t_b), Y, t_b), c_minus(c_plus(c_0, Y, t_b), X, t_b))
% 1.40/0.43 = { by axiom 12 (cls_OrderedGroup_Ocompare__rls__3_0) }
% 1.40/0.43 c_minus(c_plus(c_0, Y, t_b), X, t_b)
% 1.40/0.43 = { by lemma 14 }
% 1.40/0.43 c_minus(Y, X, t_b)
% 1.40/0.43
% 1.40/0.43 Lemma 19: c_minus(c_plus(X, Y, t_b), X, t_b) = Y.
% 1.40/0.43 Proof:
% 1.40/0.43 c_minus(c_plus(X, Y, t_b), X, t_b)
% 1.40/0.43 = { by axiom 12 (cls_OrderedGroup_Ocompare__rls__3_0) R->L }
% 1.40/0.43 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_minus(X, X, t_b), Y, t_b), c_minus(c_plus(X, Y, t_b), X, t_b))
% 1.40/0.43 = { by lemma 15 }
% 1.40/0.43 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_0, Y, t_b), c_minus(c_plus(X, Y, t_b), X, t_b))
% 1.40/0.43 = { by axiom 2 (ifeq_axiom) R->L }
% 1.40/0.43 ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_0, Y, t_b), c_minus(c_plus(X, Y, t_b), X, t_b))
% 1.40/0.43 = { by axiom 1 (tfree_tcs) R->L }
% 1.40/0.43 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_0, Y, t_b), c_minus(c_plus(X, Y, t_b), X, t_b))
% 1.40/0.43 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_4) }
% 1.40/0.43 ifeq2(true, true, c_plus(c_0, Y, t_b), c_minus(c_plus(X, Y, t_b), X, t_b))
% 1.40/0.43 = { by axiom 3 (ifeq_axiom) }
% 1.40/0.43 c_plus(c_0, Y, t_b)
% 1.40/0.43 = { by lemma 14 }
% 1.40/0.43 Y
% 1.40/0.43
% 1.40/0.43 Lemma 20: c_minus(c_plus(X, Y, t_b), Y, t_b) = c_minus(X, c_0, t_b).
% 1.40/0.43 Proof:
% 1.40/0.43 c_minus(c_plus(X, Y, t_b), Y, t_b)
% 1.40/0.43 = { by axiom 10 (cls_OrderedGroup_Ocompare__rls__5_0) R->L }
% 1.40/0.43 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_minus(X, c_minus(Y, Y, t_b), t_b), c_minus(c_plus(X, Y, t_b), Y, t_b))
% 1.40/0.43 = { by lemma 15 }
% 1.40/0.43 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_minus(X, c_0, t_b), c_minus(c_plus(X, Y, t_b), Y, t_b))
% 1.40/0.43 = { by axiom 2 (ifeq_axiom) R->L }
% 1.40/0.43 ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_minus(X, c_0, t_b), c_minus(c_plus(X, Y, t_b), Y, t_b))
% 1.40/0.43 = { by axiom 1 (tfree_tcs) R->L }
% 1.40/0.43 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_minus(X, c_0, t_b), c_minus(c_plus(X, Y, t_b), Y, t_b))
% 1.40/0.43 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_4) }
% 1.40/0.43 ifeq2(true, true, c_minus(X, c_0, t_b), c_minus(c_plus(X, Y, t_b), Y, t_b))
% 1.40/0.43 = { by axiom 3 (ifeq_axiom) }
% 1.40/0.44 c_minus(X, c_0, t_b)
% 1.40/0.44
% 1.40/0.44 Lemma 21: c_plus(c_minus(X, c_plus(X, Y, t_b), t_b), Y, t_b) = c_0.
% 1.40/0.44 Proof:
% 1.40/0.44 c_plus(c_minus(X, c_plus(X, Y, t_b), t_b), Y, t_b)
% 1.40/0.44 = { by axiom 3 (ifeq_axiom) R->L }
% 1.40/0.44 ifeq2(true, true, c_plus(c_minus(X, c_plus(X, Y, t_b), t_b), Y, t_b), c_0)
% 1.40/0.44 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 1.40/0.44 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_minus(X, c_plus(X, Y, t_b), t_b), Y, t_b), c_0)
% 1.40/0.44 = { by axiom 1 (tfree_tcs) }
% 1.40/0.44 ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_minus(X, c_plus(X, Y, t_b), t_b), Y, t_b), c_0)
% 1.40/0.44 = { by axiom 2 (ifeq_axiom) }
% 1.40/0.44 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_minus(X, c_plus(X, Y, t_b), t_b), Y, t_b), c_0)
% 1.40/0.44 = { by lemma 15 R->L }
% 1.40/0.44 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_minus(X, c_plus(X, Y, t_b), t_b), Y, t_b), c_minus(c_plus(X, Y, t_b), c_plus(X, Y, t_b), t_b))
% 1.40/0.44 = { by axiom 12 (cls_OrderedGroup_Ocompare__rls__3_0) }
% 1.40/0.44 c_minus(c_plus(X, Y, t_b), c_plus(X, Y, t_b), t_b)
% 1.40/0.44 = { by lemma 15 }
% 1.40/0.44 c_0
% 1.40/0.44
% 1.40/0.44 Lemma 22: c_minus(X, c_plus(X, Y, t_b), t_b) = c_minus(c_0, Y, t_b).
% 1.40/0.44 Proof:
% 1.40/0.44 c_minus(X, c_plus(X, Y, t_b), t_b)
% 1.40/0.44 = { by lemma 19 R->L }
% 1.40/0.44 c_minus(c_plus(c_0, c_minus(X, c_plus(X, Y, t_b), t_b), t_b), c_0, t_b)
% 1.40/0.44 = { by lemma 14 }
% 1.40/0.44 c_minus(c_minus(X, c_plus(X, Y, t_b), t_b), c_0, t_b)
% 1.40/0.44 = { by lemma 20 R->L }
% 1.40/0.44 c_minus(c_plus(c_minus(X, c_plus(X, Y, t_b), t_b), Y, t_b), Y, t_b)
% 1.40/0.44 = { by lemma 21 }
% 1.40/0.44 c_minus(c_0, Y, t_b)
% 1.40/0.44
% 1.40/0.44 Lemma 23: c_minus(X, c_minus(X, Y, t_b), t_b) = Y.
% 1.40/0.44 Proof:
% 1.40/0.44 c_minus(X, c_minus(X, Y, t_b), t_b)
% 1.40/0.44 = { by axiom 3 (ifeq_axiom) R->L }
% 1.40/0.44 ifeq2(true, true, c_minus(X, c_minus(X, Y, t_b), t_b), Y)
% 1.40/0.44 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 1.40/0.44 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_minus(X, c_minus(X, Y, t_b), t_b), Y)
% 1.40/0.44 = { by axiom 1 (tfree_tcs) }
% 1.40/0.44 ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_minus(X, c_minus(X, Y, t_b), t_b), Y)
% 1.40/0.44 = { by axiom 2 (ifeq_axiom) }
% 1.40/0.44 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_minus(X, c_minus(X, Y, t_b), t_b), Y)
% 1.40/0.44 = { by lemma 19 R->L }
% 1.40/0.44 ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_minus(X, c_minus(X, Y, t_b), t_b), c_minus(c_plus(X, Y, t_b), X, t_b))
% 1.40/0.44 = { by axiom 10 (cls_OrderedGroup_Ocompare__rls__5_0) }
% 1.40/0.44 c_minus(c_plus(X, Y, t_b), X, t_b)
% 1.40/0.44 = { by lemma 19 }
% 1.40/0.44 Y
% 1.40/0.44
% 1.40/0.44 Lemma 24: c_minus(X, c_minus(c_0, Y, t_b), t_b) = c_plus(X, Y, t_b).
% 1.40/0.44 Proof:
% 1.40/0.44 c_minus(X, c_minus(c_0, Y, t_b), t_b)
% 1.40/0.44 = { by lemma 22 R->L }
% 1.40/0.44 c_minus(X, c_minus(X, c_plus(X, Y, t_b), t_b), t_b)
% 1.40/0.44 = { by lemma 23 }
% 1.40/0.44 c_plus(X, Y, t_b)
% 1.40/0.44
% 1.40/0.44 Lemma 25: c_minus(Z, c_minus(Y, X, t_b), t_b) = c_minus(X, c_minus(Y, Z, t_b), t_b).
% 1.40/0.44 Proof:
% 1.40/0.44 c_minus(Z, c_minus(Y, X, t_b), t_b)
% 1.40/0.44 = { by lemma 18 R->L }
% 1.40/0.44 c_plus(c_minus(c_0, c_minus(Y, X, t_b), t_b), Z, t_b)
% 1.40/0.44 = { by axiom 3 (ifeq_axiom) R->L }
% 1.40/0.44 c_plus(ifeq2(true, true, c_minus(c_0, c_minus(Y, X, t_b), t_b), c_minus(X, Y, t_b)), Z, t_b)
% 1.40/0.44 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 1.40/0.44 c_plus(ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_minus(c_0, c_minus(Y, X, t_b), t_b), c_minus(X, Y, t_b)), Z, t_b)
% 1.40/0.44 = { by axiom 1 (tfree_tcs) }
% 1.40/0.44 c_plus(ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_minus(c_0, c_minus(Y, X, t_b), t_b), c_minus(X, Y, t_b)), Z, t_b)
% 1.40/0.44 = { by axiom 2 (ifeq_axiom) }
% 1.40/0.44 c_plus(ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_minus(c_0, c_minus(Y, X, t_b), t_b), c_minus(X, Y, t_b)), Z, t_b)
% 1.40/0.44 = { by lemma 14 R->L }
% 1.40/0.44 c_plus(ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_minus(c_0, c_minus(Y, X, t_b), t_b), c_minus(c_plus(c_0, X, t_b), Y, t_b)), Z, t_b)
% 1.40/0.44 = { by axiom 10 (cls_OrderedGroup_Ocompare__rls__5_0) }
% 1.40/0.44 c_plus(c_minus(c_plus(c_0, X, t_b), Y, t_b), Z, t_b)
% 1.40/0.44 = { by lemma 14 }
% 1.40/0.44 c_plus(c_minus(X, Y, t_b), Z, t_b)
% 1.40/0.44 = { by lemma 17 }
% 1.40/0.44 c_minus(X, c_minus(Y, Z, t_b), t_b)
% 1.40/0.44
% 1.40/0.44 Goal 1 (cls_conjecture_3): c_lessequals(c_minus(v_f(v_x), v_k(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = true.
% 1.40/0.44 Proof:
% 1.40/0.44 c_lessequals(c_minus(v_f(v_x), v_k(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 1.40/0.44 = { by lemma 23 R->L }
% 1.40/0.44 c_lessequals(c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_f(v_x), v_k(v_x), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 1.40/0.44 = { by lemma 25 }
% 1.40/0.44 c_lessequals(c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), c_minus(v_f(v_x), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 1.40/0.44 = { by lemma 23 }
% 1.40/0.44 c_lessequals(c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(v_k(v_x), v_g(v_x), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 1.40/0.44 = { by lemma 25 }
% 1.40/0.44 c_lessequals(c_minus(v_g(v_x), c_minus(v_k(v_x), 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), t_b)
% 1.40/0.44 = { by lemma 17 R->L }
% 1.40/0.44 c_lessequals(c_plus(c_minus(v_g(v_x), v_k(v_x), t_b), 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), t_b)
% 1.40/0.44 = { by axiom 2 (ifeq_axiom) R->L }
% 1.40/0.44 ifeq(true, true, c_lessequals(c_plus(c_minus(v_g(v_x), v_k(v_x), t_b), 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), t_b), true)
% 1.40/0.44 = { by axiom 13 (cls_OrderedGroup_Ocompare__rls__8_1) R->L }
% 1.40/0.44 ifeq(ifeq(c_lessequals(v_g(v_x), c_plus(c_0, v_k(v_x), t_b), t_b), true, ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_0, t_b), true), true), true, c_lessequals(c_plus(c_minus(v_g(v_x), v_k(v_x), t_b), 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), t_b), true)
% 1.40/0.44 = { by lemma 14 }
% 1.40/0.44 ifeq(ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_0, t_b), true), true), true, c_lessequals(c_plus(c_minus(v_g(v_x), v_k(v_x), t_b), 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), t_b), true)
% 1.40/0.44 = { by axiom 2 (ifeq_axiom) R->L }
% 1.40/0.44 ifeq(ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(ifeq(true, true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_0, t_b), true), true), true, c_lessequals(c_plus(c_minus(v_g(v_x), v_k(v_x), t_b), 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), t_b), true)
% 1.40/0.44 = { by axiom 1 (tfree_tcs) R->L }
% 1.40/0.44 ifeq(ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_0, t_b), true), true), true, c_lessequals(c_plus(c_minus(v_g(v_x), v_k(v_x), t_b), 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), t_b), true)
% 1.40/0.44 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_54) }
% 1.40/0.44 ifeq(ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(true, true, c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_0, t_b), true), true), true, c_lessequals(c_plus(c_minus(v_g(v_x), v_k(v_x), t_b), 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), t_b), true)
% 1.40/0.44 = { by axiom 2 (ifeq_axiom) }
% 1.40/0.44 ifeq(ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_0, t_b), true), true, c_lessequals(c_plus(c_minus(v_g(v_x), v_k(v_x), t_b), 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), t_b), true)
% 1.40/0.44 = { by axiom 4 (cls_conjecture_1) }
% 1.40/0.44 ifeq(ifeq(true, true, c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_0, t_b), true), true, c_lessequals(c_plus(c_minus(v_g(v_x), v_k(v_x), t_b), 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), t_b), true)
% 1.40/0.44 = { by axiom 2 (ifeq_axiom) }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_0, t_b), true, c_lessequals(c_plus(c_minus(v_g(v_x), v_k(v_x), t_b), 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), t_b), true)
% 1.40/0.45 = { by lemma 24 R->L }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_0, t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(c_0, 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), t_b), true)
% 1.40/0.45 = { by lemma 22 R->L }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_0, t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by lemma 21 R->L }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_minus(X, c_plus(X, 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), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by lemma 24 R->L }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_minus(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by lemma 17 R->L }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_minus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by lemma 20 R->L }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_minus(c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), Y, t_b), Y, t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by axiom 11 (cls_OrderedGroup_Ocompare__rls__2_0) R->L }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_minus(Y, Y, t_b), t_b), c_minus(c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), Y, t_b), Y, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by lemma 20 }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_minus(Y, Y, t_b), t_b), c_minus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by axiom 2 (ifeq_axiom) R->L }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_minus(Y, Y, t_b), t_b), c_minus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by axiom 1 (tfree_tcs) R->L }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_minus(Y, Y, t_b), t_b), c_minus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_4) }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(true, true, c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_minus(Y, Y, t_b), t_b), c_minus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by axiom 3 (ifeq_axiom) }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_minus(Y, Y, t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by lemma 15 }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by lemma 19 R->L }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_minus(c_plus(c_0, c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), t_b), c_0, t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by axiom 11 (cls_OrderedGroup_Ocompare__rls__2_0) R->L }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_0, c_minus(c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), c_0, t_b), t_b), c_minus(c_plus(c_0, c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), t_b), c_0, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by lemma 19 }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_0, c_minus(c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), c_0, t_b), t_b), c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by axiom 2 (ifeq_axiom) R->L }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_0, c_minus(c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), c_0, t_b), t_b), c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by axiom 1 (tfree_tcs) R->L }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_0, c_minus(c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), c_0, t_b), t_b), c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_4) }
% 1.40/0.45 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(true, true, c_plus(c_0, c_minus(c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), c_0, t_b), t_b), c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.45 = { by axiom 3 (ifeq_axiom) }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_plus(c_0, c_minus(c_plus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), c_0, t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.46 = { by lemma 20 }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_plus(c_0, c_minus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.46 = { by axiom 3 (ifeq_axiom) R->L }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(true, true, c_plus(c_0, c_minus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), t_b), c_minus(c_plus(c_0, c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_0, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.46 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_0, c_minus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), t_b), c_minus(c_plus(c_0, c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_0, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.46 = { by axiom 1 (tfree_tcs) }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(c_0, c_minus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), t_b), c_minus(c_plus(c_0, c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_0, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.46 = { by axiom 2 (ifeq_axiom) }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(c_0, c_minus(c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), c_0, t_b), t_b), c_minus(c_plus(c_0, c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_0, t_b)), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.46 = { by axiom 11 (cls_OrderedGroup_Ocompare__rls__2_0) }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_minus(c_plus(c_0, c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_0, t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.46 = { by lemma 16 }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_minus(c_0, c_minus(c_0, c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.46 = { by lemma 18 }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(c_0, c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.46 = { by lemma 24 }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 1.40/0.46 = { by axiom 2 (ifeq_axiom) R->L }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), t_b), true, ifeq(true, true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true), true)
% 1.40/0.46 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_54) R->L }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), t_b), true, ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true), true)
% 1.40/0.46 = { by axiom 1 (tfree_tcs) }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), t_b), true, ifeq(ifeq(true, true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true), true)
% 1.40/0.46 = { by axiom 2 (ifeq_axiom) }
% 1.40/0.46 ifeq(c_lessequals(c_minus(v_g(v_x), v_k(v_x), t_b), c_plus(c_minus(v_f(v_x), v_g(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), t_b), true, ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, c_lessequals(c_minus(c_minus(v_g(v_x), v_k(v_x), t_b), c_minus(X, c_plus(X, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true), true)
% 1.40/0.46 = { by axiom 13 (cls_OrderedGroup_Ocompare__rls__8_1) }
% 1.40/0.46 true
% 1.40/0.46 % SZS output end Proof
% 1.40/0.46
% 1.40/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------