%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA032-2 : 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 09:30:39 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.34s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA032-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n013.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 20:31:51 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.34 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
% 0.23/0.34
% 0.23/0.34 % SZS status Unsatisfiable
% 0.23/0.34
% 0.23/0.35 % SZS output start Proof
% 0.23/0.35 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.23/0.35 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.23/0.35 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.23/0.35 Axiom 4 (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.
% 0.23/0.35 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_21): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Osemigroup__mult(X), true) = true.
% 0.23/0.35 Axiom 6 (clsrel_Ring__and__Field_Oordered__idom_17): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Oab__semigroup__mult(X), true) = true.
% 0.23/0.35 Axiom 7 (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.
% 0.23/0.35 Axiom 8 (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.
% 0.23/0.35 Axiom 9 (cls_OrderedGroup_Omult__ac__2_0): ifeq2(class_OrderedGroup_Oab__semigroup__mult(X), true, c_times(Y, Z, X), c_times(Z, Y, X)) = c_times(Z, Y, X).
% 0.23/0.35 Axiom 10 (cls_conjecture_0): c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b) = true.
% 0.23/0.35 Axiom 11 (cls_OrderedGroup_Omult__ac__1_0): ifeq2(class_OrderedGroup_Osemigroup__mult(X), true, c_times(c_times(Y, Z, X), W, X), c_times(Y, c_times(Z, W, X), X)) = c_times(Y, c_times(Z, W, X), X).
% 0.23/0.35 Axiom 12 (cls_Ring__and__Field_Opordered__semiring__class_Omult__left__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(Y, Z, X), c_times(Y, W, X), X), true), true), true) = true.
% 0.23/0.35
% 0.23/0.35 Lemma 13: c_times(X, Y, t_b) = c_times(Y, X, t_b).
% 0.23/0.35 Proof:
% 0.23/0.35 c_times(X, Y, t_b)
% 0.23/0.35 = { by axiom 9 (cls_OrderedGroup_Omult__ac__2_0) R->L }
% 0.23/0.35 ifeq2(class_OrderedGroup_Oab__semigroup__mult(t_b), true, c_times(Y, X, t_b), c_times(X, Y, t_b))
% 0.23/0.35 = { by axiom 2 (ifeq_axiom) R->L }
% 0.23/0.35 ifeq2(ifeq(true, true, class_OrderedGroup_Oab__semigroup__mult(t_b), true), true, c_times(Y, X, t_b), c_times(X, Y, t_b))
% 0.23/0.35 = { by axiom 1 (tfree_tcs) R->L }
% 0.23/0.35 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__semigroup__mult(t_b), true), true, c_times(Y, X, t_b), c_times(X, Y, t_b))
% 0.23/0.35 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_17) }
% 0.23/0.35 ifeq2(true, true, c_times(Y, X, t_b), c_times(X, Y, t_b))
% 0.23/0.35 = { by axiom 3 (ifeq_axiom) }
% 0.23/0.35 c_times(Y, X, t_b)
% 0.23/0.35
% 0.23/0.35 Goal 1 (cls_conjecture_1): c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_c, c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b) = true.
% 0.23/0.35 Proof:
% 0.23/0.35 c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_c, c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)
% 0.23/0.35 = { by lemma 13 R->L }
% 0.23/0.35 c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), v_c, t_b), t_b)
% 0.23/0.35 = { by axiom 3 (ifeq_axiom) R->L }
% 0.23/0.35 c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), ifeq2(true, true, c_times(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), v_c, t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(c_HOL_Oabs(v_g(v_x), t_b), v_c, t_b), t_b)), t_b)
% 0.23/0.35 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_21) R->L }
% 0.23/0.35 c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Osemigroup__mult(t_b), true), true, c_times(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), v_c, t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(c_HOL_Oabs(v_g(v_x), t_b), v_c, t_b), t_b)), t_b)
% 0.23/0.35 = { by axiom 1 (tfree_tcs) }
% 0.23/0.35 c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), ifeq2(ifeq(true, true, class_OrderedGroup_Osemigroup__mult(t_b), true), true, c_times(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), v_c, t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(c_HOL_Oabs(v_g(v_x), t_b), v_c, t_b), t_b)), t_b)
% 0.23/0.35 = { by axiom 2 (ifeq_axiom) }
% 0.23/0.35 c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), ifeq2(class_OrderedGroup_Osemigroup__mult(t_b), true, c_times(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), v_c, t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(c_HOL_Oabs(v_g(v_x), t_b), v_c, t_b), t_b)), t_b)
% 0.23/0.35 = { by axiom 11 (cls_OrderedGroup_Omult__ac__1_0) }
% 0.23/0.35 c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(c_HOL_Oabs(v_g(v_x), t_b), v_c, t_b), t_b), t_b)
% 0.23/0.35 = { by lemma 13 }
% 0.23/0.35 c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)
% 0.23/0.35 = { by lemma 13 }
% 0.23/0.35 c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b)
% 0.23/0.35 = { by axiom 2 (ifeq_axiom) R->L }
% 0.23/0.35 ifeq(true, true, c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true)
% 0.23/0.35 = { by axiom 10 (cls_conjecture_0) R->L }
% 0.23/0.35 ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true)
% 0.23/0.35 = { by lemma 13 R->L }
% 0.23/0.35 ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_b(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true)
% 0.23/0.35 = { by lemma 13 R->L }
% 0.23/0.35 ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true)
% 0.23/0.35 = { by axiom 2 (ifeq_axiom) R->L }
% 0.23/0.35 ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true)
% 0.23/0.35 = { by axiom 2 (ifeq_axiom) R->L }
% 0.23/0.35 ifeq(true, true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true)
% 0.23/0.35 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_42) R->L }
% 0.23/0.35 ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_Ring__and__Field_Opordered__semiring(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true)
% 0.23/0.35 = { by axiom 1 (tfree_tcs) }
% 0.23/0.35 ifeq(ifeq(true, true, class_Ring__and__Field_Opordered__semiring(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true)
% 0.23/0.35 = { by axiom 2 (ifeq_axiom) }
% 0.23/0.35 ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true)
% 0.23/0.35 = { by axiom 8 (cls_OrderedGroup_Oabs__ge__zero_0) R->L }
% 0.23/0.35 ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, ifeq(ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_b), t_b), true), true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true)
% 0.23/0.35 = { by axiom 2 (ifeq_axiom) R->L }
% 0.23/0.35 ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, ifeq(ifeq(ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_b), t_b), true), true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true)
% 0.23/0.35 = { by axiom 1 (tfree_tcs) R->L }
% 0.23/0.35 ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_b), t_b), true), true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true)
% 0.23/0.35 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 0.23/0.35 ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, ifeq(ifeq(true, true, c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_b), t_b), true), true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true)
% 0.23/0.35 = { by axiom 2 (ifeq_axiom) }
% 0.23/0.35 ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_b), t_b), true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true)
% 0.23/0.35 = { by axiom 12 (cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) }
% 0.23/0.35 true
% 0.23/0.35 % SZS output end Proof
% 0.23/0.35
% 0.23/0.35 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------