TSTP Solution File: ANA020-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA020-2 : 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 : n019.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 17:21:05 EDT 2023
% Result : Unsatisfiable 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA020-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 18:42:58 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.41 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.22/0.41
% 0.22/0.41 % SZS status Unsatisfiable
% 0.22/0.41
% 0.22/0.42 % SZS output start Proof
% 0.22/0.42 Take the following subset of the input axioms:
% 0.22/0.42 fof(cls_OrderedGroup_Oabs__eq__0_1, axiom, ![T_a]: (~class_OrderedGroup_Olordered__ab__group__abs(T_a) | c_HOL_Oabs(c_0, T_a)=c_0)).
% 0.22/0.42 fof(cls_OrderedGroup_Oabs__ge__zero_0, axiom, ![V_a, T_a2]: (~class_OrderedGroup_Olordered__ab__group__abs(T_a2) | c_lessequals(c_0, c_HOL_Oabs(V_a, T_a2), T_a2))).
% 0.22/0.42 fof(cls_Orderings_Oorder__less__imp__le_0, axiom, ![V_x, V_y, T_a2]: (~class_Orderings_Oorder(T_a2) | (~c_less(V_x, V_y, T_a2) | c_lessequals(V_x, V_y, T_a2)))).
% 0.22/0.42 fof(cls_Ring__and__Field_Omult__nonneg__nonneg_0, axiom, ![V_b, T_a2, V_a2]: (~class_Ring__and__Field_Opordered__cancel__semiring(T_a2) | (~c_lessequals(c_0, V_b, T_a2) | (~c_lessequals(c_0, V_a2, T_a2) | c_lessequals(c_0, c_times(V_a2, V_b, T_a2), T_a2))))).
% 0.22/0.42 fof(cls_conjecture_0, negated_conjecture, v_f(c_0)=c_0).
% 0.22/0.42 fof(cls_conjecture_1, negated_conjecture, c_less(c_0, v_c, t_a)).
% 0.22/0.42 fof(cls_conjecture_3, negated_conjecture, v_x=c_0).
% 0.22/0.42 fof(cls_conjecture_4, negated_conjecture, ~c_lessequals(c_HOL_Oabs(v_f(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)).
% 0.22/0.42 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))).
% 0.22/0.42 fof(clsrel_Ring__and__Field_Oordered__idom_44, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_Orderings_Oorder(T2))).
% 0.22/0.42 fof(clsrel_Ring__and__Field_Oordered__idom_50, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_OrderedGroup_Olordered__ab__group__abs(T2))).
% 0.22/0.42 fof(tfree_tcs, negated_conjecture, class_Ring__and__Field_Oordered__idom(t_a)).
% 0.22/0.42
% 0.22/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.42 fresh(y, y, x1...xn) = u
% 0.22/0.42 C => fresh(s, t, x1...xn) = v
% 0.22/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.42 variables of u and v.
% 0.22/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.42 input problem has no model of domain size 1).
% 0.22/0.42
% 0.22/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.42
% 0.22/0.42 Axiom 1 (cls_conjecture_3): v_x = c_0.
% 0.22/0.42 Axiom 2 (cls_conjecture_0): v_f(c_0) = c_0.
% 0.22/0.42 Axiom 3 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_a) = true.
% 0.22/0.42 Axiom 4 (cls_conjecture_1): c_less(c_0, v_c, t_a) = true.
% 0.22/0.42 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_50): fresh(X, X, Y) = true.
% 0.22/0.42 Axiom 6 (cls_OrderedGroup_Oabs__eq__0_1): fresh7(X, X, Y) = c_0.
% 0.22/0.42 Axiom 7 (clsrel_Ring__and__Field_Oordered__idom_40): fresh3(X, X, Y) = true.
% 0.22/0.42 Axiom 8 (clsrel_Ring__and__Field_Oordered__idom_44): fresh2(X, X, Y) = true.
% 0.22/0.42 Axiom 9 (clsrel_Ring__and__Field_Oordered__idom_50): fresh(class_Ring__and__Field_Oordered__idom(X), true, X) = class_OrderedGroup_Olordered__ab__group__abs(X).
% 0.22/0.42 Axiom 10 (cls_OrderedGroup_Oabs__ge__zero_0): fresh8(X, X, Y, Z) = true.
% 0.22/0.42 Axiom 11 (cls_OrderedGroup_Oabs__eq__0_1): fresh7(class_OrderedGroup_Olordered__ab__group__abs(X), true, X) = c_HOL_Oabs(c_0, X).
% 0.22/0.42 Axiom 12 (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).
% 0.22/0.42 Axiom 13 (clsrel_Ring__and__Field_Oordered__idom_44): fresh2(class_Ring__and__Field_Oordered__idom(X), true, X) = class_Orderings_Oorder(X).
% 0.22/0.42 Axiom 14 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): fresh10(X, X, Y, Z, W) = true.
% 0.22/0.42 Axiom 15 (cls_OrderedGroup_Oabs__ge__zero_0): fresh8(class_OrderedGroup_Olordered__ab__group__abs(X), true, X, Y) = c_lessequals(c_0, c_HOL_Oabs(Y, X), X).
% 0.22/0.42 Axiom 16 (cls_Orderings_Oorder__less__imp__le_0): fresh6(X, X, Y, Z, W) = c_lessequals(Z, W, Y).
% 0.22/0.42 Axiom 17 (cls_Orderings_Oorder__less__imp__le_0): fresh5(X, X, Y, Z, W) = true.
% 0.22/0.42 Axiom 18 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): fresh4(X, X, Y, Z, W) = c_lessequals(c_0, c_times(W, Z, Y), Y).
% 0.22/0.42 Axiom 19 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): fresh9(X, X, Y, Z, W) = fresh10(c_lessequals(c_0, Z, Y), true, Y, Z, W).
% 0.22/0.42 Axiom 20 (cls_Orderings_Oorder__less__imp__le_0): fresh6(class_Orderings_Oorder(X), true, X, Y, Z) = fresh5(c_less(Y, Z, X), true, X, Y, Z).
% 0.22/0.42 Axiom 21 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): fresh9(class_Ring__and__Field_Opordered__cancel__semiring(X), true, X, Y, Z) = fresh4(c_lessequals(c_0, Z, X), true, X, Y, Z).
% 0.22/0.42
% 0.22/0.42 Lemma 22: class_OrderedGroup_Olordered__ab__group__abs(t_a) = true.
% 0.22/0.42 Proof:
% 0.22/0.42 class_OrderedGroup_Olordered__ab__group__abs(t_a)
% 0.22/0.42 = { by axiom 9 (clsrel_Ring__and__Field_Oordered__idom_50) R->L }
% 0.22/0.42 fresh(class_Ring__and__Field_Oordered__idom(t_a), true, t_a)
% 0.22/0.42 = { by axiom 3 (tfree_tcs) }
% 0.22/0.42 fresh(true, true, t_a)
% 0.22/0.42 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 0.22/0.42 true
% 0.22/0.42
% 0.22/0.42 Goal 1 (cls_conjecture_4): c_lessequals(c_HOL_Oabs(v_f(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a) = true.
% 0.22/0.42 Proof:
% 0.22/0.42 c_lessequals(c_HOL_Oabs(v_f(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.22/0.42 = { by axiom 1 (cls_conjecture_3) }
% 0.22/0.42 c_lessequals(c_HOL_Oabs(v_f(c_0), t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.22/0.42 = { by axiom 2 (cls_conjecture_0) }
% 0.22/0.42 c_lessequals(c_HOL_Oabs(c_0, t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.22/0.42 = { by axiom 11 (cls_OrderedGroup_Oabs__eq__0_1) R->L }
% 0.22/0.42 c_lessequals(fresh7(class_OrderedGroup_Olordered__ab__group__abs(t_a), true, t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.22/0.42 = { by lemma 22 }
% 0.22/0.42 c_lessequals(fresh7(true, true, t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.22/0.42 = { by axiom 6 (cls_OrderedGroup_Oabs__eq__0_1) }
% 0.22/0.42 c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)
% 0.22/0.42 = { by axiom 18 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) R->L }
% 0.22/0.42 fresh4(true, true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 17 (cls_Orderings_Oorder__less__imp__le_0) R->L }
% 0.22/0.42 fresh4(fresh5(true, true, t_a, c_0, v_c), true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 4 (cls_conjecture_1) R->L }
% 0.22/0.42 fresh4(fresh5(c_less(c_0, v_c, t_a), true, t_a, c_0, v_c), true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 20 (cls_Orderings_Oorder__less__imp__le_0) R->L }
% 0.22/0.42 fresh4(fresh6(class_Orderings_Oorder(t_a), true, t_a, c_0, v_c), true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 13 (clsrel_Ring__and__Field_Oordered__idom_44) R->L }
% 0.22/0.42 fresh4(fresh6(fresh2(class_Ring__and__Field_Oordered__idom(t_a), true, t_a), true, t_a, c_0, v_c), true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 3 (tfree_tcs) }
% 0.22/0.42 fresh4(fresh6(fresh2(true, true, t_a), true, t_a, c_0, v_c), true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 8 (clsrel_Ring__and__Field_Oordered__idom_44) }
% 0.22/0.42 fresh4(fresh6(true, true, t_a, c_0, v_c), true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 16 (cls_Orderings_Oorder__less__imp__le_0) }
% 0.22/0.42 fresh4(c_lessequals(c_0, v_c, t_a), true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 21 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) R->L }
% 0.22/0.42 fresh9(class_Ring__and__Field_Opordered__cancel__semiring(t_a), true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 12 (clsrel_Ring__and__Field_Oordered__idom_40) R->L }
% 0.22/0.42 fresh9(fresh3(class_Ring__and__Field_Oordered__idom(t_a), true, t_a), true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 3 (tfree_tcs) }
% 0.22/0.42 fresh9(fresh3(true, true, t_a), true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_40) }
% 0.22/0.42 fresh9(true, true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 19 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) }
% 0.22/0.42 fresh10(c_lessequals(c_0, c_HOL_Oabs(v_h(v_x), t_a), t_a), true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 15 (cls_OrderedGroup_Oabs__ge__zero_0) R->L }
% 0.22/0.42 fresh10(fresh8(class_OrderedGroup_Olordered__ab__group__abs(t_a), true, t_a, v_h(v_x)), true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by lemma 22 }
% 0.22/0.42 fresh10(fresh8(true, true, t_a, v_h(v_x)), true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 10 (cls_OrderedGroup_Oabs__ge__zero_0) }
% 0.22/0.42 fresh10(true, true, t_a, c_HOL_Oabs(v_h(v_x), t_a), v_c)
% 0.22/0.42 = { by axiom 14 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) }
% 0.22/0.42 true
% 0.22/0.42 % SZS output end Proof
% 0.22/0.42
% 0.22/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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