TSTP Solution File: ANA044-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA044-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 17:21:13 EDT 2023
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA044-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 18:41:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.39 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.39
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 Take the following subset of the input axioms:
% 0.20/0.40 fof(cls_OrderedGroup_Oabs__of__nonneg_0, axiom, ![T_a, V_y]: (~class_OrderedGroup_Olordered__ab__group__abs(T_a) | (~c_lessequals(c_0, V_y, T_a) | c_HOL_Oabs(V_y, T_a)=V_y))).
% 0.20/0.40 fof(cls_Ring__and__Field_Omult__nonneg__nonneg_0, axiom, ![V_b, V_a, T_a2]: (~class_Ring__and__Field_Opordered__cancel__semiring(T_a2) | (~c_lessequals(c_0, V_b, T_a2) | (~c_lessequals(c_0, V_a, T_a2) | c_lessequals(c_0, c_times(V_a, V_b, T_a2), T_a2))))).
% 0.20/0.40 fof(cls_conjecture_0, negated_conjecture, ![V_U, V_V]: c_lessequals(c_0, v_l(V_U, V_V), t_b)).
% 0.20/0.40 fof(cls_conjecture_1, negated_conjecture, ![V_U2]: c_lessequals(c_0, v_h(V_U2), t_b)).
% 0.20/0.40 fof(cls_conjecture_3, negated_conjecture, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b)!=c_HOL_Oabs(c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b), t_b)).
% 0.20/0.40 fof(clsrel_Ring__and__Field_Oordered__idom_40, axiom, ![T]: (~class_Ring__and__Field_Oordered__idom(T) | class_Ring__and__Field_Opordered__cancel__semiring(T))).
% 0.20/0.40 fof(clsrel_Ring__and__Field_Oordered__idom_50, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_OrderedGroup_Olordered__ab__group__abs(T2))).
% 0.20/0.40 fof(tfree_tcs, negated_conjecture, class_Ring__and__Field_Oordered__idom(t_b)).
% 0.20/0.40
% 0.20/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.40 fresh(y, y, x1...xn) = u
% 0.20/0.40 C => fresh(s, t, x1...xn) = v
% 0.20/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.40 variables of u and v.
% 0.20/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.40 input problem has no model of domain size 1).
% 0.20/0.40
% 0.20/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.40
% 0.20/0.40 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.20/0.40 Axiom 2 (clsrel_Ring__and__Field_Oordered__idom_40): fresh3(X, X, Y) = true.
% 0.20/0.40 Axiom 3 (clsrel_Ring__and__Field_Oordered__idom_50): fresh2(X, X, Y) = true.
% 0.20/0.40 Axiom 4 (cls_conjecture_1): c_lessequals(c_0, v_h(X), t_b) = true.
% 0.20/0.40 Axiom 5 (cls_OrderedGroup_Oabs__of__nonneg_0): fresh(X, X, Y, Z) = Z.
% 0.20/0.40 Axiom 6 (cls_OrderedGroup_Oabs__of__nonneg_0): fresh4(X, X, Y, Z) = c_HOL_Oabs(Z, Y).
% 0.20/0.40 Axiom 7 (clsrel_Ring__and__Field_Oordered__idom_40): fresh3(class_Ring__and__Field_Oordered__idom(X), true, X) = class_Ring__and__Field_Opordered__cancel__semiring(X).
% 0.20/0.40 Axiom 8 (clsrel_Ring__and__Field_Oordered__idom_50): fresh2(class_Ring__and__Field_Oordered__idom(X), true, X) = class_OrderedGroup_Olordered__ab__group__abs(X).
% 0.20/0.40 Axiom 9 (cls_conjecture_0): c_lessequals(c_0, v_l(X, Y), t_b) = true.
% 0.20/0.40 Axiom 10 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): fresh7(X, X, Y, Z, W) = true.
% 0.20/0.40 Axiom 11 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): fresh5(X, X, Y, Z, W) = c_lessequals(c_0, c_times(W, Z, Y), Y).
% 0.20/0.40 Axiom 12 (cls_OrderedGroup_Oabs__of__nonneg_0): fresh4(class_OrderedGroup_Olordered__ab__group__abs(X), true, X, Y) = fresh(c_lessequals(c_0, Y, X), true, X, Y).
% 0.20/0.40 Axiom 13 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): fresh6(X, X, Y, Z, W) = fresh7(c_lessequals(c_0, Z, Y), true, Y, Z, W).
% 0.20/0.40 Axiom 14 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): fresh6(class_Ring__and__Field_Opordered__cancel__semiring(X), true, X, Y, Z) = fresh5(c_lessequals(c_0, Z, X), true, X, Y, Z).
% 0.20/0.40
% 0.20/0.40 Goal 1 (cls_conjecture_3): c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b) = c_HOL_Oabs(c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b), t_b).
% 0.20/0.40 Proof:
% 0.20/0.40 c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b)
% 0.20/0.40 = { by axiom 5 (cls_OrderedGroup_Oabs__of__nonneg_0) R->L }
% 0.20/0.40 fresh(true, true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 10 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) R->L }
% 0.20/0.40 fresh(fresh7(true, true, t_b, v_h(v_k(v_x, v_xa)), v_l(v_x, v_xa)), true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 4 (cls_conjecture_1) R->L }
% 0.20/0.40 fresh(fresh7(c_lessequals(c_0, v_h(v_k(v_x, v_xa)), t_b), true, t_b, v_h(v_k(v_x, v_xa)), v_l(v_x, v_xa)), true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 13 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) R->L }
% 0.20/0.40 fresh(fresh6(true, true, t_b, v_h(v_k(v_x, v_xa)), v_l(v_x, v_xa)), true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 2 (clsrel_Ring__and__Field_Oordered__idom_40) R->L }
% 0.20/0.40 fresh(fresh6(fresh3(true, true, t_b), true, t_b, v_h(v_k(v_x, v_xa)), v_l(v_x, v_xa)), true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 1 (tfree_tcs) R->L }
% 0.20/0.40 fresh(fresh6(fresh3(class_Ring__and__Field_Oordered__idom(t_b), true, t_b), true, t_b, v_h(v_k(v_x, v_xa)), v_l(v_x, v_xa)), true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_40) }
% 0.20/0.40 fresh(fresh6(class_Ring__and__Field_Opordered__cancel__semiring(t_b), true, t_b, v_h(v_k(v_x, v_xa)), v_l(v_x, v_xa)), true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 14 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) }
% 0.20/0.40 fresh(fresh5(c_lessequals(c_0, v_l(v_x, v_xa), t_b), true, t_b, v_h(v_k(v_x, v_xa)), v_l(v_x, v_xa)), true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 9 (cls_conjecture_0) }
% 0.20/0.40 fresh(fresh5(true, true, t_b, v_h(v_k(v_x, v_xa)), v_l(v_x, v_xa)), true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 11 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) }
% 0.20/0.40 fresh(c_lessequals(c_0, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b), t_b), true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 12 (cls_OrderedGroup_Oabs__of__nonneg_0) R->L }
% 0.20/0.40 fresh4(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 8 (clsrel_Ring__and__Field_Oordered__idom_50) R->L }
% 0.20/0.40 fresh4(fresh2(class_Ring__and__Field_Oordered__idom(t_b), true, t_b), true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 1 (tfree_tcs) }
% 0.20/0.40 fresh4(fresh2(true, true, t_b), true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 3 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 0.20/0.40 fresh4(true, true, t_b, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b))
% 0.20/0.40 = { by axiom 6 (cls_OrderedGroup_Oabs__of__nonneg_0) }
% 0.20/0.40 c_HOL_Oabs(c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b), t_b)
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40
% 0.20/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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