%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA010-2 : 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 09:30:35 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.26s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA010-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n010.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 20:28:32 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.26 Command-line arguments: --no-flatten-goal
% 0.20/0.26
% 0.20/0.26 % SZS status Unsatisfiable
% 0.20/0.26
% 0.20/0.27 % SZS output start Proof
% 0.20/0.27 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.20/0.27 Axiom 2 (cls_conjecture_0): c_lessequals(c_0, v_f(X), t_b) = true.
% 0.20/0.27 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.20/0.27 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.20/0.27 Axiom 5 (clsrel_OrderedGroup_Olordered__ab__group__abs_17): ifeq(class_OrderedGroup_Olordered__ab__group__abs(X), true, class_Orderings_Oorder(X), true) = true.
% 0.20/0.27 Axiom 6 (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.
% 0.20/0.27 Axiom 7 (cls_conjecture_1): c_lessequals(v_f(X), c_times(v_c, v_g(X), t_b), t_b) = true.
% 0.20/0.27 Axiom 8 (cls_OrderedGroup_Oabs__of__nonneg_0): ifeq2(c_lessequals(c_0, X, Y), true, ifeq2(class_OrderedGroup_Olordered__ab__group__abs(Y), true, c_HOL_Oabs(X, Y), X), X) = X.
% 0.20/0.27 Axiom 9 (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).
% 0.20/0.27 Axiom 10 (cls_Orderings_Oorder__class_Oorder__trans_0): ifeq(class_Orderings_Oorder(X), true, ifeq(c_lessequals(Y, Z, X), true, ifeq(c_lessequals(Z, W, X), true, c_lessequals(Y, W, X), true), true), true) = true.
% 0.20/0.27
% 0.20/0.27 Goal 1 (cls_conjecture_2): c_lessequals(v_f(v_x(X)), c_times(X, c_HOL_Oabs(v_g(v_x(X)), t_b), t_b), t_b) = true.
% 0.20/0.27 The goal is true when:
% 0.20/0.27 X = c_HOL_Oabs(v_c, t_b)
% 0.20/0.27
% 0.20/0.27 Proof:
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), t_b)
% 0.20/0.27 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(true, true, c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)), t_b)
% 0.20/0.27 = { by axiom 1 (tfree_tcs) R->L }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(class_Ring__and__Field_Oordered__idom(t_b), true, c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)), t_b)
% 0.20/0.27 = { by axiom 9 (cls_Ring__and__Field_Oabs__mult_0) }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), t_b)
% 0.20/0.27 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(true, true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_50) R->L }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 1 (tfree_tcs) }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 4 (ifeq_axiom) }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(true, true, ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 10 (cls_Orderings_Oorder__class_Oorder__trans_0) R->L }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b), true, ifeq(c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true, c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true), true), true), true, ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 2 (cls_conjecture_0) }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(ifeq(class_Orderings_Oorder(t_b), true, ifeq(true, true, ifeq(c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true, c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true), true), true), true, ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 4 (ifeq_axiom) R->L }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(ifeq(ifeq(true, true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true, c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true), true), true), true, ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_50) R->L }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true, c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true), true), true), true, ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 1 (tfree_tcs) }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(ifeq(ifeq(ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true, c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true), true), true), true, ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 4 (ifeq_axiom) }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(ifeq(ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true, c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true), true), true), true, ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 5 (clsrel_OrderedGroup_Olordered__ab__group__abs_17) }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(ifeq(true, true, ifeq(true, true, ifeq(c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true, c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true), true), true), true, ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 4 (ifeq_axiom) }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(ifeq(true, true, ifeq(c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true, c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true), true), true, ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 4 (ifeq_axiom) }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(ifeq(c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true, c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true), true, ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 7 (cls_conjecture_1) }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(ifeq(true, true, c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true), true, ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 4 (ifeq_axiom) }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), ifeq2(c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true, ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.20/0.27 = { by axiom 8 (cls_OrderedGroup_Oabs__of__nonneg_0) }
% 0.20/0.27 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)
% 0.20/0.27 = { by axiom 7 (cls_conjecture_1) }
% 0.20/0.27 true
% 0.20/0.27 % SZS output end Proof
% 0.20/0.27
% 0.20/0.27 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------