%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 09:30:35 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.25s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n006.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 20:26:39 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.25 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.10/0.25
% 0.10/0.25 % SZS status Unsatisfiable
% 0.10/0.25
% 0.10/0.25 % SZS output start Proof
% 0.10/0.25 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.10/0.25 Axiom 2 (cls_conjecture_0): c_lessequals(v_lb(X), v_f(X), t_b) = true.
% 0.10/0.25 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.10/0.25 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.10/0.25 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_37): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X), true) = true.
% 0.10/0.25 Axiom 6 (clsrel_Ring__and__Field_Oordered__idom_4): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Oab__group__add(X), true) = true.
% 0.10/0.25 Axiom 7 (cls_OrderedGroup_Oright__minus_0): ifeq2(class_OrderedGroup_Oab__group__add(X), true, c_plus(Y, c_uminus(Y, X), X), c_0) = c_0.
% 0.10/0.25 Axiom 8 (cls_OrderedGroup_Oadd__le__cancel__right_1): ifeq(c_lessequals(X, Y, Z), true, ifeq(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(Z), true, c_lessequals(c_plus(X, W, Z), c_plus(Y, W, Z), Z), true), true) = true.
% 0.10/0.25
% 0.10/0.25 Goal 1 (cls_conjecture_2): c_lessequals(c_0, c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b) = true.
% 0.10/0.25 Proof:
% 0.10/0.25 c_lessequals(c_0, c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)
% 0.10/0.25 = { by axiom 7 (cls_OrderedGroup_Oright__minus_0) R->L }
% 0.10/0.25 c_lessequals(ifeq2(class_OrderedGroup_Oab__group__add(t_b), true, c_plus(v_lb(v_x), c_uminus(v_lb(v_x), t_b), t_b), c_0), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)
% 0.10/0.25 = { by axiom 3 (ifeq_axiom) R->L }
% 0.10/0.25 c_lessequals(ifeq2(ifeq(true, true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(v_lb(v_x), c_uminus(v_lb(v_x), t_b), t_b), c_0), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)
% 0.10/0.25 = { by axiom 1 (tfree_tcs) R->L }
% 0.10/0.25 c_lessequals(ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__group__add(t_b), true), true, c_plus(v_lb(v_x), c_uminus(v_lb(v_x), t_b), t_b), c_0), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)
% 0.10/0.25 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_4) }
% 0.10/0.25 c_lessequals(ifeq2(true, true, c_plus(v_lb(v_x), c_uminus(v_lb(v_x), t_b), t_b), c_0), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)
% 0.10/0.25 = { by axiom 4 (ifeq_axiom) }
% 0.10/0.25 c_lessequals(c_plus(v_lb(v_x), c_uminus(v_lb(v_x), t_b), t_b), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)
% 0.10/0.25 = { by axiom 3 (ifeq_axiom) R->L }
% 0.10/0.25 ifeq(true, true, c_lessequals(c_plus(v_lb(v_x), c_uminus(v_lb(v_x), t_b), t_b), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b), true)
% 0.10/0.25 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_37) R->L }
% 0.10/0.25 ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b), true), true, c_lessequals(c_plus(v_lb(v_x), c_uminus(v_lb(v_x), t_b), t_b), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b), true)
% 0.10/0.25 = { by axiom 1 (tfree_tcs) }
% 0.10/0.25 ifeq(ifeq(true, true, class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b), true), true, c_lessequals(c_plus(v_lb(v_x), c_uminus(v_lb(v_x), t_b), t_b), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b), true)
% 0.10/0.25 = { by axiom 3 (ifeq_axiom) }
% 0.10/0.25 ifeq(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b), true, c_lessequals(c_plus(v_lb(v_x), c_uminus(v_lb(v_x), t_b), t_b), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b), true)
% 0.10/0.25 = { by axiom 3 (ifeq_axiom) R->L }
% 0.10/0.25 ifeq(true, true, ifeq(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b), true, c_lessequals(c_plus(v_lb(v_x), c_uminus(v_lb(v_x), t_b), t_b), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b), true), true)
% 0.10/0.25 = { by axiom 2 (cls_conjecture_0) R->L }
% 0.10/0.25 ifeq(c_lessequals(v_lb(v_x), v_f(v_x), t_b), true, ifeq(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b), true, c_lessequals(c_plus(v_lb(v_x), c_uminus(v_lb(v_x), t_b), t_b), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b), true), true)
% 0.10/0.25 = { by axiom 8 (cls_OrderedGroup_Oadd__le__cancel__right_1) }
% 0.10/0.25 true
% 0.10/0.25 % SZS output end Proof
% 0.10/0.25
% 0.10/0.25 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------