%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA020-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 09:30:37 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.26s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA020-2 : 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 : n019.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 20:29:33 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.26 Command-line arguments: --no-flatten-goal
% 0.09/0.26
% 0.09/0.26 % SZS status Unsatisfiable
% 0.09/0.26
% 0.09/0.26 % SZS output start Proof
% 0.09/0.26 Axiom 1 (cls_conjecture_3): v_x = c_0.
% 0.09/0.26 Axiom 2 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_a) = true.
% 0.09/0.26 Axiom 3 (cls_conjecture_0): v_f(c_0) = c_0.
% 0.09/0.27 Axiom 4 (cls_conjecture_1): c_less(c_0, v_c, t_a) = true.
% 0.09/0.27 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.09/0.27 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.09/0.27 Axiom 7 (clsrel_Ring__and__Field_Oordered__idom_44): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_Orderings_Oorder(X), true) = true.
% 0.09/0.27 Axiom 8 (clsrel_Ring__and__Field_Oordered__idom_40): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_Ring__and__Field_Opordered__cancel__semiring(X), true) = true.
% 0.09/0.27 Axiom 9 (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.
% 0.09/0.27 Axiom 10 (cls_OrderedGroup_Oabs__eq__0_1): ifeq2(class_OrderedGroup_Olordered__ab__group__abs(X), true, c_HOL_Oabs(c_0, X), c_0) = c_0.
% 0.09/0.27 Axiom 11 (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.
% 0.09/0.27 Axiom 12 (cls_Orderings_Oorder__less__imp__le_0): ifeq(class_Orderings_Oorder(X), true, ifeq(c_less(Y, Z, X), true, c_lessequals(Y, Z, X), true), true) = true.
% 0.09/0.27 Axiom 13 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X), true, ifeq(c_lessequals(c_0, Y, X), true, ifeq(c_lessequals(c_0, Z, X), true, c_lessequals(c_0, c_times(Y, Z, X), X), true), true), true) = true.
% 0.09/0.27
% 0.09/0.27 Goal 1 (cls_conjecture_4): c_lessequals(c_HOL_Oabs(v_f(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a) = true.
% 0.09/0.27 Proof:
% 0.09/0.27 c_lessequals(c_HOL_Oabs(v_f(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.09/0.27 = { by axiom 1 (cls_conjecture_3) }
% 0.09/0.27 c_lessequals(c_HOL_Oabs(v_f(c_0), t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.09/0.27 = { by axiom 3 (cls_conjecture_0) }
% 0.09/0.27 c_lessequals(c_HOL_Oabs(c_0, t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.09/0.27 = { by axiom 1 (cls_conjecture_3) R->L }
% 0.09/0.27 c_lessequals(c_HOL_Oabs(v_x, t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.09/0.27 = { by axiom 5 (ifeq_axiom) R->L }
% 0.09/0.27 c_lessequals(ifeq2(true, true, c_HOL_Oabs(v_x, t_a), v_x), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.09/0.27 = { by axiom 9 (clsrel_Ring__and__Field_Oordered__idom_50) R->L }
% 0.09/0.27 c_lessequals(ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_a), true, class_OrderedGroup_Olordered__ab__group__abs(t_a), true), true, c_HOL_Oabs(v_x, t_a), v_x), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.09/0.27 = { by axiom 2 (tfree_tcs) }
% 0.09/0.27 c_lessequals(ifeq2(ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_a), true), true, c_HOL_Oabs(v_x, t_a), v_x), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.09/0.27 = { by axiom 6 (ifeq_axiom) }
% 0.09/0.27 c_lessequals(ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_a), true, c_HOL_Oabs(v_x, t_a), v_x), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.09/0.27 = { by axiom 1 (cls_conjecture_3) }
% 0.09/0.27 c_lessequals(ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_a), true, c_HOL_Oabs(c_0, t_a), v_x), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.09/0.27 = { by axiom 1 (cls_conjecture_3) }
% 0.09/0.27 c_lessequals(ifeq2(class_OrderedGroup_Olordered__ab__group__abs(t_a), true, c_HOL_Oabs(c_0, t_a), c_0), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.09/0.27 = { by axiom 10 (cls_OrderedGroup_Oabs__eq__0_1) }
% 0.09/0.27 c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.09/0.27 = { by axiom 1 (cls_conjecture_3) R->L }
% 0.09/0.27 c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.09/0.27 = { by axiom 6 (ifeq_axiom) R->L }
% 0.09/0.27 ifeq(true, true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true)
% 0.09/0.27 = { by axiom 11 (cls_OrderedGroup_Oabs__ge__zero_0) R->L }
% 0.09/0.27 ifeq(ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_a), true, c_lessequals(c_0, c_HOL_Oabs(v_h(v_x), t_a), t_a), true), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true)
% 0.09/0.27 = { by axiom 1 (cls_conjecture_3) R->L }
% 0.09/0.27 ifeq(ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_a), true, c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true)
% 0.09/0.27 = { by axiom 6 (ifeq_axiom) R->L }
% 0.09/0.27 ifeq(ifeq(ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_a), true), true, c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true)
% 0.09/0.27 = { by axiom 2 (tfree_tcs) R->L }
% 0.09/0.27 ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_a), true, class_OrderedGroup_Olordered__ab__group__abs(t_a), true), true, c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true)
% 0.09/0.27 = { by axiom 9 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 0.09/0.27 ifeq(ifeq(true, true, c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true)
% 0.09/0.27 = { by axiom 6 (ifeq_axiom) }
% 0.09/0.27 ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true)
% 0.09/0.27 = { by axiom 6 (ifeq_axiom) R->L }
% 0.09/0.27 ifeq(true, true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true)
% 0.09/0.27 = { by axiom 6 (ifeq_axiom) R->L }
% 0.09/0.27 ifeq(true, true, ifeq(true, true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 8 (clsrel_Ring__and__Field_Oordered__idom_40) R->L }
% 0.09/0.27 ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_a), true, class_Ring__and__Field_Opordered__cancel__semiring(t_a), true), true, ifeq(true, true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 2 (tfree_tcs) }
% 0.09/0.27 ifeq(ifeq(true, true, class_Ring__and__Field_Opordered__cancel__semiring(t_a), true), true, ifeq(true, true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 6 (ifeq_axiom) }
% 0.09/0.27 ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_a), true, ifeq(true, true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 12 (cls_Orderings_Oorder__less__imp__le_0) R->L }
% 0.09/0.27 ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_a), true, ifeq(ifeq(class_Orderings_Oorder(t_a), true, ifeq(c_less(v_x, v_c, t_a), true, c_lessequals(v_x, v_c, t_a), true), true), true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 1 (cls_conjecture_3) }
% 0.09/0.27 ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_a), true, ifeq(ifeq(class_Orderings_Oorder(t_a), true, ifeq(c_less(c_0, v_c, t_a), true, c_lessequals(v_x, v_c, t_a), true), true), true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 4 (cls_conjecture_1) }
% 0.09/0.27 ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_a), true, ifeq(ifeq(class_Orderings_Oorder(t_a), true, ifeq(true, true, c_lessequals(v_x, v_c, t_a), true), true), true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 6 (ifeq_axiom) R->L }
% 0.09/0.27 ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_a), true, ifeq(ifeq(ifeq(true, true, class_Orderings_Oorder(t_a), true), true, ifeq(true, true, c_lessequals(v_x, v_c, t_a), true), true), true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 2 (tfree_tcs) R->L }
% 0.09/0.27 ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_a), true, ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_a), true, class_Orderings_Oorder(t_a), true), true, ifeq(true, true, c_lessequals(v_x, v_c, t_a), true), true), true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_44) }
% 0.09/0.27 ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_a), true, ifeq(ifeq(true, true, ifeq(true, true, c_lessequals(v_x, v_c, t_a), true), true), true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 6 (ifeq_axiom) }
% 0.09/0.27 ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_a), true, ifeq(ifeq(true, true, c_lessequals(v_x, v_c, t_a), true), true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 6 (ifeq_axiom) }
% 0.09/0.27 ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_a), true, ifeq(c_lessequals(v_x, v_c, t_a), true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 1 (cls_conjecture_3) }
% 0.09/0.27 ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_a), true, ifeq(c_lessequals(c_0, v_c, t_a), true, ifeq(c_lessequals(v_x, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 1 (cls_conjecture_3) }
% 0.09/0.27 ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_a), true, ifeq(c_lessequals(c_0, v_c, t_a), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 1 (cls_conjecture_3) }
% 0.09/0.27 ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_a), true, ifeq(c_lessequals(c_0, v_c, t_a), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a), true), true), true)
% 0.09/0.27 = { by axiom 13 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) }
% 0.09/0.27 true
% 0.09/0.27 % SZS output end Proof
% 0.09/0.27
% 0.09/0.27 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------