%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA027-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 09:30:38 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.27s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA027-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n010.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 20:31:17 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 Command-line arguments: --no-flatten-goal
% 0.20/0.27
% 0.20/0.27 % SZS status Unsatisfiable
% 0.20/0.27
% 0.20/0.28 % SZS output start Proof
% 0.20/0.28 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.20/0.28 Axiom 2 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.20/0.28 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.20/0.28 Axiom 4 (cls_conjecture_2): c_lessequals(v_g(v_x), v_k(v_x), t_b) = true.
% 0.20/0.28 Axiom 5 (clsrel_OrderedGroup_Olordered__ab__group__abs_15): ifeq(class_OrderedGroup_Olordered__ab__group__abs(X), true, class_LOrder_Ojoin__semilorder(X), true) = true.
% 0.20/0.28 Axiom 6 (clsrel_OrderedGroup_Olordered__ab__group__abs_1): ifeq(class_OrderedGroup_Olordered__ab__group__abs(X), true, class_OrderedGroup_Opordered__ab__group__add(X), true) = true.
% 0.20/0.28 Axiom 7 (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.
% 0.20/0.28 Axiom 8 (clsrel_LOrder_Ojoin__semilorder_1): ifeq(class_LOrder_Ojoin__semilorder(X), true, class_Orderings_Oorder(X), true) = true.
% 0.20/0.29 Axiom 9 (clsrel_Ring__and__Field_Oordered__idom_23): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Ocomm__monoid__add(X), true) = true.
% 0.20/0.29 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.
% 0.20/0.29 Axiom 11 (cls_conjecture_1): c_lessequals(c_0, c_minus(v_f(v_x), v_k(v_x), t_b), t_b) = true.
% 0.20/0.29 Axiom 12 (cls_OrderedGroup_Ocompare__rls__9_0): ifeq(class_OrderedGroup_Opordered__ab__group__add(X), true, ifeq(c_lessequals(Y, c_minus(Z, W, X), X), true, c_lessequals(c_plus(Y, W, X), Z, X), true), true) = true.
% 0.20/0.29 Axiom 13 (cls_OrderedGroup_Ocompare__rls__9_1): ifeq(class_OrderedGroup_Opordered__ab__group__add(X), true, ifeq(c_lessequals(c_plus(Y, Z, X), W, X), true, c_lessequals(Y, c_minus(W, Z, X), X), true), true) = true.
% 0.20/0.29 Axiom 14 (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.
% 0.20/0.29
% 0.20/0.29 Lemma 15: c_plus(c_0, X, t_b) = X.
% 0.20/0.29 Proof:
% 0.20/0.29 c_plus(c_0, X, t_b)
% 0.20/0.29 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.29 ifeq2(true, true, c_plus(c_0, X, t_b), X)
% 0.20/0.29 = { by axiom 9 (clsrel_Ring__and__Field_Oordered__idom_23) R->L }
% 0.20/0.29 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)
% 0.20/0.29 = { by axiom 1 (tfree_tcs) }
% 0.20/0.29 ifeq2(ifeq(true, true, class_OrderedGroup_Ocomm__monoid__add(t_b), true), true, c_plus(c_0, X, t_b), X)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.29 ifeq2(class_OrderedGroup_Ocomm__monoid__add(t_b), true, c_plus(c_0, X, t_b), X)
% 0.20/0.29 = { by axiom 10 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) }
% 0.20/0.29 X
% 0.20/0.29
% 0.20/0.29 Goal 1 (cls_conjecture_3): c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = true.
% 0.20/0.29 Proof:
% 0.20/0.29 c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.29 ifeq(true, true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.29 = { by axiom 14 (cls_Orderings_Oorder__class_Oorder__trans_0) R->L }
% 0.20/0.29 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)
% 0.20/0.29 = { by lemma 15 R->L }
% 0.20/0.29 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(c_plus(c_0, v_k(v_x), t_b), 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)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.29 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(ifeq(true, true, c_lessequals(c_plus(c_0, v_k(v_x), t_b), v_f(v_x), t_b), true), 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)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.29 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(ifeq(true, true, ifeq(true, true, c_lessequals(c_plus(c_0, v_k(v_x), t_b), v_f(v_x), t_b), true), true), 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)
% 0.20/0.29 = { by axiom 6 (clsrel_OrderedGroup_Olordered__ab__group__abs_1) R->L }
% 0.20/0.29 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(ifeq(ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, ifeq(true, true, c_lessequals(c_plus(c_0, v_k(v_x), t_b), v_f(v_x), t_b), true), true), 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)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.29 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(ifeq(ifeq(ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, ifeq(true, true, c_lessequals(c_plus(c_0, v_k(v_x), t_b), v_f(v_x), t_b), true), true), 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)
% 0.20/0.29 = { by axiom 1 (tfree_tcs) R->L }
% 0.20/0.29 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, ifeq(true, true, c_lessequals(c_plus(c_0, v_k(v_x), t_b), v_f(v_x), t_b), true), true), 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)
% 0.20/0.29 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 0.20/0.29 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(ifeq(ifeq(true, true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, ifeq(true, true, c_lessequals(c_plus(c_0, v_k(v_x), t_b), v_f(v_x), t_b), true), true), 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)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.29 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(true, true, c_lessequals(c_plus(c_0, v_k(v_x), t_b), v_f(v_x), t_b), true), true), 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)
% 0.20/0.29 = { by axiom 11 (cls_conjecture_1) R->L }
% 0.20/0.29 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(c_lessequals(c_0, c_minus(v_f(v_x), v_k(v_x), t_b), t_b), true, c_lessequals(c_plus(c_0, v_k(v_x), t_b), v_f(v_x), t_b), true), true), 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)
% 0.20/0.29 = { by axiom 12 (cls_OrderedGroup_Ocompare__rls__9_0) }
% 0.20/0.29 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(true, 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)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.29 ifeq(ifeq(ifeq(true, true, class_Orderings_Oorder(t_b), true), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(true, 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)
% 0.20/0.29 = { by axiom 5 (clsrel_OrderedGroup_Olordered__ab__group__abs_15) R->L }
% 0.20/0.29 ifeq(ifeq(ifeq(ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, class_LOrder_Ojoin__semilorder(t_b), true), true, class_Orderings_Oorder(t_b), true), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(true, 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)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.29 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, class_LOrder_Ojoin__semilorder(t_b), true), true, class_Orderings_Oorder(t_b), true), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(true, 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)
% 0.20/0.29 = { by axiom 1 (tfree_tcs) R->L }
% 0.20/0.29 ifeq(ifeq(ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, class_LOrder_Ojoin__semilorder(t_b), true), true, class_Orderings_Oorder(t_b), true), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(true, 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)
% 0.20/0.29 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 0.20/0.29 ifeq(ifeq(ifeq(ifeq(true, true, class_LOrder_Ojoin__semilorder(t_b), true), true, class_Orderings_Oorder(t_b), true), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(true, 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)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.29 ifeq(ifeq(ifeq(class_LOrder_Ojoin__semilorder(t_b), true, class_Orderings_Oorder(t_b), true), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(true, 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)
% 0.20/0.29 = { by axiom 8 (clsrel_LOrder_Ojoin__semilorder_1) }
% 0.20/0.29 ifeq(ifeq(true, true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(true, 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)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.29 ifeq(ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(true, 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)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.29 ifeq(ifeq(c_lessequals(v_g(v_x), v_k(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)
% 0.20/0.29 = { by axiom 4 (cls_conjecture_2) }
% 0.20/0.29 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)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.29 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)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.29 ifeq(true, true, 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), true)
% 0.20/0.29 = { by axiom 6 (clsrel_OrderedGroup_Olordered__ab__group__abs_1) R->L }
% 0.20/0.29 ifeq(ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, 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), true)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.29 ifeq(ifeq(ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, 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), true)
% 0.20/0.29 = { by axiom 1 (tfree_tcs) R->L }
% 0.20/0.29 ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, 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), true)
% 0.20/0.29 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 0.20/0.29 ifeq(ifeq(true, true, class_OrderedGroup_Opordered__ab__group__add(t_b), true), true, 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), true)
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.29 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, 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), true)
% 0.20/0.29 = { by lemma 15 R->L }
% 0.20/0.29 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(c_lessequals(c_plus(c_0, v_g(v_x), t_b), 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), true)
% 0.20/0.29 = { by axiom 13 (cls_OrderedGroup_Ocompare__rls__9_1) }
% 0.20/0.29 true
% 0.20/0.29 % SZS output end Proof
% 0.20/0.29
% 0.20/0.29 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------