%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA023-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 0.08s 0.26s
% Output : Proof 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA023-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n011.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 20:30:18 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.26 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
% 0.08/0.26
% 0.08/0.26 % SZS status Unsatisfiable
% 0.08/0.26
% 0.08/0.27 % SZS output start Proof
% 0.08/0.27 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.08/0.27 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.08/0.27 Axiom 3 (cls_conjecture_2): c_lessequals(v_k(v_x), v_f(v_x), t_b) = true.
% 0.08/0.27 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.08/0.27 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_54): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Opordered__ab__group__add(X), true) = true.
% 0.08/0.27 Axiom 6 (clsrel_Ring__and__Field_Oordered__idom_23): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Ocomm__monoid__add(X), true) = true.
% 0.08/0.27 Axiom 7 (clsrel_Ring__and__Field_Oordered__idom_33): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_Orderings_Olinorder(X), true) = true.
% 0.08/0.27 Axiom 8 (clsrel_Orderings_Olinorder_4): ifeq(class_Orderings_Olinorder(X), true, class_Orderings_Oorder(X), true) = true.
% 0.08/0.27 Axiom 9 (cls_conjecture_1): c_lessequals(c_0, c_minus(v_k(v_x), v_g(v_x), t_b), t_b) = true.
% 0.08/0.27 Axiom 10 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0): ifeq2(class_OrderedGroup_Ocomm__monoid__add(X), true, c_plus(c_0, Y, X), Y) = Y.
% 0.08/0.27 Axiom 11 (cls_OrderedGroup_Ocompare__rls__9_0): ifeq(c_lessequals(X, c_minus(Y, Z, W), W), true, ifeq(class_OrderedGroup_Opordered__ab__group__add(W), true, c_lessequals(c_plus(X, Z, W), Y, W), true), true) = true.
% 0.08/0.27 Axiom 12 (cls_OrderedGroup_Ocompare__rls__9_1): ifeq(c_lessequals(c_plus(X, Y, Z), W, Z), true, ifeq(class_OrderedGroup_Opordered__ab__group__add(Z), true, c_lessequals(X, c_minus(W, Y, Z), Z), true), true) = true.
% 0.08/0.27 Axiom 13 (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.
% 0.08/0.27
% 0.08/0.27 Lemma 14: c_plus(c_0, X, t_b) = X.
% 0.08/0.27 Proof:
% 0.08/0.27 c_plus(c_0, X, t_b)
% 0.08/0.27 = { by axiom 4 (ifeq_axiom) R->L }
% 0.08/0.27 ifeq2(true, true, c_plus(c_0, X, t_b), X)
% 0.08/0.27 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_23) R->L }
% 0.08/0.27 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Ocomm__monoid__add(t_b), true), true, c_plus(c_0, X, t_b), X)
% 0.08/0.27 = { by axiom 1 (tfree_tcs) }
% 0.08/0.27 ifeq2(ifeq(true, true, class_OrderedGroup_Ocomm__monoid__add(t_b), true), true, c_plus(c_0, X, t_b), X)
% 0.08/0.27 = { by axiom 2 (ifeq_axiom) }
% 0.08/0.27 ifeq2(class_OrderedGroup_Ocomm__monoid__add(t_b), true, c_plus(c_0, X, t_b), X)
% 0.08/0.27 = { by axiom 10 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) }
% 0.08/0.27 X
% 0.08/0.27
% 0.08/0.27 Goal 1 (cls_conjecture_3): c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = true.
% 0.08/0.27 Proof:
% 0.08/0.27 c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 0.08/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.28 ifeq(true, true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 13 (cls_Orderings_Oorder__class_Oorder__trans_0) R->L }
% 0.08/0.28 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by lemma 14 R->L }
% 0.08/0.28 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_k(v_x), t_b), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.28 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(ifeq(true, true, c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_k(v_x), t_b), true), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_54) R->L }
% 0.08/0.28 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_k(v_x), t_b), true), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 1 (tfree_tcs) }
% 0.08/0.28 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(ifeq(ifeq(true, true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_k(v_x), t_b), true), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.08/0.28 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_k(v_x), t_b), true), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.28 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(ifeq(true, true, ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_k(v_x), t_b), true), true), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 9 (cls_conjecture_1) R->L }
% 0.08/0.28 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(ifeq(c_lessequals(c_0, c_minus(v_k(v_x), v_g(v_x), t_b), t_b), true, ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_k(v_x), t_b), true), true), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 11 (cls_OrderedGroup_Ocompare__rls__9_0) }
% 0.08/0.28 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.28 ifeq(ifeq(ifeq(true, true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_33) R->L }
% 0.08/0.28 ifeq(ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_Orderings_Olinorder(t_b), true), true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 1 (tfree_tcs) }
% 0.08/0.28 ifeq(ifeq(ifeq(ifeq(true, true, class_Orderings_Olinorder(t_b), true), true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.08/0.28 ifeq(ifeq(ifeq(class_Orderings_Olinorder(t_b), true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 8 (clsrel_Orderings_Olinorder_4) }
% 0.08/0.28 ifeq(ifeq(true, true, ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.08/0.28 ifeq(ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.08/0.28 ifeq(ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 3 (cls_conjecture_2) }
% 0.08/0.28 ifeq(ifeq(true, true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.08/0.28 ifeq(c_lessequals(v_g(v_x), v_f(v_x), t_b), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.08/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.28 ifeq(c_lessequals(v_g(v_x), v_f(v_x), t_b), true, ifeq(true, true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true), true)
% 0.08/0.28 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_54) R->L }
% 0.08/0.28 ifeq(c_lessequals(v_g(v_x), v_f(v_x), t_b), true, ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true), true)
% 0.08/0.28 = { by axiom 1 (tfree_tcs) }
% 0.08/0.28 ifeq(c_lessequals(v_g(v_x), v_f(v_x), t_b), true, ifeq(ifeq(true, true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true), true)
% 0.08/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.08/0.28 ifeq(c_lessequals(v_g(v_x), v_f(v_x), t_b), true, ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true), true)
% 0.08/0.28 = { by lemma 14 R->L }
% 0.08/0.28 ifeq(c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_f(v_x), t_b), true, ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true), true)
% 0.08/0.28 = { by axiom 12 (cls_OrderedGroup_Ocompare__rls__9_1) }
% 0.08/0.28 true
% 0.08/0.28 % SZS output end Proof
% 0.08/0.28
% 0.08/0.28 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------