%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA039-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 09:30:40 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.31s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA039-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n013.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 20:33:06 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.31 Command-line arguments: --no-flatten-goal
% 0.21/0.31
% 0.21/0.31 % SZS status Unsatisfiable
% 0.21/0.31
% 0.21/0.32 % SZS output start Proof
% 0.21/0.32 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_a) = true.
% 0.21/0.32 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.21/0.32 Axiom 3 (clsrel_Ring__and__Field_Oordered__idom_44): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_Orderings_Oorder(X), true) = true.
% 0.21/0.32 Axiom 4 (clsrel_Ring__and__Field_Oordered__idom_42): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_Ring__and__Field_Opordered__semiring(X), true) = true.
% 0.21/0.32 Axiom 5 (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.
% 0.21/0.32 Axiom 6 (cls_OrderedGroup_Oabs__ge__self_0): ifeq(class_OrderedGroup_Olordered__ab__group__abs(X), true, c_lessequals(Y, c_HOL_Oabs(Y, X), X), true) = true.
% 0.21/0.32 Axiom 7 (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.
% 0.21/0.32 Axiom 8 (cls_conjecture_0): c_lessequals(c_HOL_Oabs(v_h(X), t_a), c_times(v_c, c_HOL_Oabs(v_f(X), t_a), t_a), t_a) = true.
% 0.21/0.32 Axiom 9 (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.
% 0.21/0.32 Axiom 10 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__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(Z, Y, X), c_times(W, Y, X), X), true), true), true) = true.
% 0.21/0.32
% 0.21/0.32 Goal 1 (cls_conjecture_2): c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a) = true.
% 0.21/0.32 Proof:
% 0.21/0.32 c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a)
% 0.21/0.32 = { by axiom 2 (ifeq_axiom) R->L }
% 0.21/0.32 ifeq(true, true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.32 = { by axiom 10 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) R->L }
% 0.21/0.32 ifeq(ifeq(class_Ring__and__Field_Opordered__semiring(t_a), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true, ifeq(c_lessequals(v_c, c_HOL_Oabs(v_c, t_a), t_a), true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.32 = { by axiom 2 (ifeq_axiom) R->L }
% 0.21/0.33 ifeq(ifeq(class_Ring__and__Field_Opordered__semiring(t_a), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true, ifeq(ifeq(true, true, c_lessequals(v_c, c_HOL_Oabs(v_c, t_a), t_a), true), true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_50) R->L }
% 0.21/0.33 ifeq(ifeq(class_Ring__and__Field_Opordered__semiring(t_a), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true, 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_c, c_HOL_Oabs(v_c, t_a), t_a), true), true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 1 (tfree_tcs) }
% 0.21/0.33 ifeq(ifeq(class_Ring__and__Field_Opordered__semiring(t_a), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true, ifeq(ifeq(ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_a), true), true, c_lessequals(v_c, c_HOL_Oabs(v_c, t_a), t_a), true), true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 2 (ifeq_axiom) }
% 0.21/0.33 ifeq(ifeq(class_Ring__and__Field_Opordered__semiring(t_a), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true, ifeq(ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_a), true, c_lessequals(v_c, c_HOL_Oabs(v_c, t_a), t_a), true), true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 6 (cls_OrderedGroup_Oabs__ge__self_0) }
% 0.21/0.33 ifeq(ifeq(class_Ring__and__Field_Opordered__semiring(t_a), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true, ifeq(true, true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 2 (ifeq_axiom) R->L }
% 0.21/0.33 ifeq(ifeq(ifeq(true, true, class_Ring__and__Field_Opordered__semiring(t_a), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true, ifeq(true, true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 1 (tfree_tcs) R->L }
% 0.21/0.33 ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_a), true, class_Ring__and__Field_Opordered__semiring(t_a), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true, ifeq(true, true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_42) }
% 0.21/0.33 ifeq(ifeq(true, true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true, ifeq(true, true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 2 (ifeq_axiom) }
% 0.21/0.33 ifeq(ifeq(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true, ifeq(true, true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 2 (ifeq_axiom) }
% 0.21/0.33 ifeq(ifeq(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 2 (ifeq_axiom) R->L }
% 0.21/0.33 ifeq(ifeq(ifeq(true, true, c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true), true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_50) R->L }
% 0.21/0.33 ifeq(ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_a), true, class_OrderedGroup_Olordered__ab__group__abs(t_a), true), true, c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true), true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 1 (tfree_tcs) }
% 0.21/0.33 ifeq(ifeq(ifeq(ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_a), true), true, c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true), true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 2 (ifeq_axiom) }
% 0.21/0.33 ifeq(ifeq(ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_a), true, c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true), true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 7 (cls_OrderedGroup_Oabs__ge__zero_0) }
% 0.21/0.33 ifeq(ifeq(true, true, c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 2 (ifeq_axiom) }
% 0.21/0.33 ifeq(c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true)
% 0.21/0.33 = { by axiom 2 (ifeq_axiom) R->L }
% 0.21/0.33 ifeq(true, true, ifeq(c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true)
% 0.21/0.33 = { by axiom 8 (cls_conjecture_0) R->L }
% 0.21/0.33 ifeq(c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, ifeq(c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true)
% 0.21/0.33 = { by axiom 2 (ifeq_axiom) R->L }
% 0.21/0.33 ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, ifeq(c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true)
% 0.21/0.33 = { by axiom 3 (clsrel_Ring__and__Field_Oordered__idom_44) R->L }
% 0.21/0.33 ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_a), true, class_Orderings_Oorder(t_a), true), true, ifeq(c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, ifeq(c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true)
% 0.21/0.33 = { by axiom 1 (tfree_tcs) }
% 0.21/0.33 ifeq(ifeq(true, true, class_Orderings_Oorder(t_a), true), true, ifeq(c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, ifeq(c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true)
% 0.21/0.34 = { by axiom 2 (ifeq_axiom) }
% 0.21/0.34 ifeq(class_Orderings_Oorder(t_a), true, ifeq(c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, ifeq(c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true), true), true)
% 0.21/0.34 = { by axiom 9 (cls_Orderings_Oorder__class_Oorder__trans_0) }
% 0.21/0.34 true
% 0.21/0.34 % SZS output end Proof
% 0.21/0.34
% 0.21/0.34 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------