%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA037-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 0.21s 0.29s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA037-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n016.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 20:38:33 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.29 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
% 0.21/0.29
% 0.21/0.29 % SZS status Unsatisfiable
% 0.21/0.29
% 0.21/0.29 % SZS output start Proof
% 0.21/0.29 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.21/0.29 Axiom 2 (cls_conjecture_2): c_lessequals(c_0, v_f(v_xa), t_b) = true.
% 0.21/0.29 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.21/0.29 Axiom 4 (clsrel_Ring__and__Field_Oordered__idom_33): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_Orderings_Olinorder(X), true) = true.
% 0.21/0.29 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_44): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_Orderings_Oorder(X), true) = true.
% 0.21/0.29 Axiom 6 (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.
% 0.21/0.29 Axiom 7 (cls_conjecture_4): c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(v_c, v_f(v_xa), t_b), t_b) = true.
% 0.21/0.29 Axiom 8 (cls_Orderings_Ole__maxI1_0): ifeq(class_Orderings_Olinorder(X), true, c_lessequals(Y, c_Orderings_Omax(Y, Z, X), X), true) = true.
% 0.21/0.29 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.
% 0.21/0.29 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.
% 0.21/0.29
% 0.21/0.29 Goal 1 (cls_conjecture_8): c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b) = true.
% 0.21/0.29 Proof:
% 0.21/0.29 c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b)
% 0.21/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.21/0.29 ifeq(true, true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.29 = { by axiom 10 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) R->L }
% 0.21/0.29 ifeq(ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, ifeq(c_lessequals(c_0, v_f(v_xa), t_b), true, ifeq(c_lessequals(v_c, c_Orderings_Omax(v_c, v_ca, t_b), t_b), true, c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true), true), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.21/0.29 ifeq(ifeq(ifeq(true, true, class_Ring__and__Field_Opordered__semiring(t_b), true), true, ifeq(c_lessequals(c_0, v_f(v_xa), t_b), true, ifeq(c_lessequals(v_c, c_Orderings_Omax(v_c, v_ca, t_b), t_b), true, c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true), true), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.29 = { by axiom 1 (tfree_tcs) R->L }
% 0.21/0.29 ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_Ring__and__Field_Opordered__semiring(t_b), true), true, ifeq(c_lessequals(c_0, v_f(v_xa), t_b), true, ifeq(c_lessequals(v_c, c_Orderings_Omax(v_c, v_ca, t_b), t_b), true, c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true), true), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.30 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_42) }
% 0.21/0.30 ifeq(ifeq(true, true, ifeq(c_lessequals(c_0, v_f(v_xa), t_b), true, ifeq(c_lessequals(v_c, c_Orderings_Omax(v_c, v_ca, t_b), t_b), true, c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true), true), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.30 = { by axiom 3 (ifeq_axiom) }
% 0.21/0.30 ifeq(ifeq(c_lessequals(c_0, v_f(v_xa), t_b), true, ifeq(c_lessequals(v_c, c_Orderings_Omax(v_c, v_ca, t_b), t_b), true, c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.30 = { by axiom 2 (cls_conjecture_2) }
% 0.21/0.30 ifeq(ifeq(true, true, ifeq(c_lessequals(v_c, c_Orderings_Omax(v_c, v_ca, t_b), t_b), true, c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.30 = { by axiom 3 (ifeq_axiom) }
% 0.21/0.30 ifeq(ifeq(c_lessequals(v_c, c_Orderings_Omax(v_c, v_ca, t_b), t_b), true, c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.30 = { by axiom 3 (ifeq_axiom) R->L }
% 0.21/0.30 ifeq(ifeq(ifeq(true, true, c_lessequals(v_c, c_Orderings_Omax(v_c, v_ca, t_b), t_b), true), true, c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.30 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_33) R->L }
% 0.21/0.30 ifeq(ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_Orderings_Olinorder(t_b), true), true, c_lessequals(v_c, c_Orderings_Omax(v_c, v_ca, t_b), t_b), true), true, c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.30 = { by axiom 1 (tfree_tcs) }
% 0.21/0.30 ifeq(ifeq(ifeq(ifeq(true, true, class_Orderings_Olinorder(t_b), true), true, c_lessequals(v_c, c_Orderings_Omax(v_c, v_ca, t_b), t_b), true), true, c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.30 = { by axiom 3 (ifeq_axiom) }
% 0.21/0.30 ifeq(ifeq(ifeq(class_Orderings_Olinorder(t_b), true, c_lessequals(v_c, c_Orderings_Omax(v_c, v_ca, t_b), t_b), true), true, c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.30 = { by axiom 8 (cls_Orderings_Ole__maxI1_0) }
% 0.21/0.30 ifeq(ifeq(true, true, c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.30 = { by axiom 3 (ifeq_axiom) }
% 0.21/0.30 ifeq(c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true)
% 0.21/0.30 = { by axiom 3 (ifeq_axiom) R->L }
% 0.21/0.30 ifeq(true, true, ifeq(c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true)
% 0.21/0.30 = { by axiom 3 (ifeq_axiom) R->L }
% 0.21/0.30 ifeq(true, true, ifeq(true, true, ifeq(c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true), true)
% 0.21/0.30 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_44) R->L }
% 0.21/0.30 ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true), true)
% 0.21/0.30 = { by axiom 1 (tfree_tcs) }
% 0.21/0.30 ifeq(ifeq(true, true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true), true)
% 0.21/0.30 = { by axiom 3 (ifeq_axiom) }
% 0.21/0.30 ifeq(class_Orderings_Oorder(t_b), true, ifeq(true, true, ifeq(c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true), true)
% 0.21/0.30 = { by axiom 7 (cls_conjecture_4) R->L }
% 0.21/0.30 ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(v_c, v_f(v_xa), t_b), t_b), true, ifeq(c_lessequals(c_times(v_c, v_f(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true, c_lessequals(c_HOL_Oabs(v_a(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_f(v_xa), t_b), t_b), true), true), true)
% 0.21/0.30 = { by axiom 9 (cls_Orderings_Oorder__class_Oorder__trans_0) }
% 0.21/0.30 true
% 0.21/0.30 % SZS output end Proof
% 0.21/0.30
% 0.21/0.30 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------