TSTP Solution File: ANA010-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA010-2 : 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 : n007.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 17:21:02 EDT 2023
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA010-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 18:06:26 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.39 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Take the following subset of the input axioms:
% 0.19/0.40 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))).
% 0.19/0.40 fof(cls_Orderings_Oorder__class_Oorder__trans_0, axiom, ![V_z, V_x, T_a2, V_y2]: (~class_Orderings_Oorder(T_a2) | (~c_lessequals(V_y2, V_z, T_a2) | (~c_lessequals(V_x, V_y2, T_a2) | c_lessequals(V_x, V_z, T_a2))))).
% 0.19/0.40 fof(cls_Ring__and__Field_Oabs__mult_0, axiom, ![V_a, V_b, T_a2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | c_HOL_Oabs(c_times(V_a, V_b, T_a2), T_a2)=c_times(c_HOL_Oabs(V_a, T_a2), c_HOL_Oabs(V_b, T_a2), T_a2))).
% 0.19/0.40 fof(cls_conjecture_0, negated_conjecture, ![V_U]: c_lessequals(c_0, v_f(V_U), t_b)).
% 0.19/0.40 fof(cls_conjecture_1, negated_conjecture, ![V_U2]: c_lessequals(v_f(V_U2), c_times(v_c, v_g(V_U2), t_b), t_b)).
% 0.19/0.40 fof(cls_conjecture_2, negated_conjecture, ![V_U2]: ~c_lessequals(v_f(v_x(V_U2)), c_times(V_U2, c_HOL_Oabs(v_g(v_x(V_U2)), t_b), t_b), t_b)).
% 0.19/0.40 fof(clsrel_OrderedGroup_Olordered__ab__group__abs_17, axiom, ![T]: (~class_OrderedGroup_Olordered__ab__group__abs(T) | class_Orderings_Oorder(T))).
% 0.19/0.40 fof(clsrel_Ring__and__Field_Oordered__idom_50, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_OrderedGroup_Olordered__ab__group__abs(T2))).
% 0.19/0.40 fof(tfree_tcs, negated_conjecture, class_Ring__and__Field_Oordered__idom(t_b)).
% 0.19/0.40
% 0.19/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.40 fresh(y, y, x1...xn) = u
% 0.19/0.40 C => fresh(s, t, x1...xn) = v
% 0.19/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.40 variables of u and v.
% 0.19/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.40 input problem has no model of domain size 1).
% 0.19/0.40
% 0.19/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.40
% 0.19/0.40 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true2.
% 0.19/0.40 Axiom 2 (clsrel_OrderedGroup_Olordered__ab__group__abs_17): fresh3(X, X, Y) = true2.
% 0.19/0.40 Axiom 3 (clsrel_Ring__and__Field_Oordered__idom_50): fresh2(X, X, Y) = true2.
% 0.19/0.40 Axiom 4 (cls_conjecture_0): c_lessequals(c_0, v_f(X), t_b) = true2.
% 0.19/0.40 Axiom 5 (cls_OrderedGroup_Oabs__of__nonneg_0): fresh(X, X, Y, Z) = Z.
% 0.19/0.40 Axiom 6 (cls_OrderedGroup_Oabs__of__nonneg_0): fresh5(X, X, Y, Z) = c_HOL_Oabs(Z, Y).
% 0.19/0.40 Axiom 7 (clsrel_OrderedGroup_Olordered__ab__group__abs_17): fresh3(class_OrderedGroup_Olordered__ab__group__abs(X), true2, X) = class_Orderings_Oorder(X).
% 0.19/0.40 Axiom 8 (clsrel_Ring__and__Field_Oordered__idom_50): fresh2(class_Ring__and__Field_Oordered__idom(X), true2, X) = class_OrderedGroup_Olordered__ab__group__abs(X).
% 0.19/0.40 Axiom 9 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh8(X, X, Y, Z, W) = true2.
% 0.19/0.40 Axiom 10 (cls_Ring__and__Field_Oabs__mult_0): fresh4(X, X, Y, Z, W) = c_HOL_Oabs(c_times(Z, W, Y), Y).
% 0.19/0.40 Axiom 11 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh6(X, X, Y, Z, W, V) = c_lessequals(V, W, Y).
% 0.19/0.40 Axiom 12 (cls_Ring__and__Field_Oabs__mult_0): fresh4(class_Ring__and__Field_Oordered__idom(X), true2, X, Y, Z) = c_times(c_HOL_Oabs(Y, X), c_HOL_Oabs(Z, X), X).
% 0.19/0.40 Axiom 13 (cls_OrderedGroup_Oabs__of__nonneg_0): fresh5(c_lessequals(c_0, X, Y), true2, Y, X) = fresh(class_OrderedGroup_Olordered__ab__group__abs(Y), true2, Y, X).
% 0.19/0.40 Axiom 14 (cls_conjecture_1): c_lessequals(v_f(X), c_times(v_c, v_g(X), t_b), t_b) = true2.
% 0.19/0.40 Axiom 15 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh7(X, X, Y, Z, W, V) = fresh8(c_lessequals(Z, W, Y), true2, Y, W, V).
% 0.19/0.40 Axiom 16 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh7(class_Orderings_Oorder(X), true2, X, Y, Z, W) = fresh6(c_lessequals(W, Y, X), true2, X, Y, Z, W).
% 0.19/0.40
% 0.19/0.40 Lemma 17: class_OrderedGroup_Olordered__ab__group__abs(t_b) = true2.
% 0.19/0.40 Proof:
% 0.19/0.40 class_OrderedGroup_Olordered__ab__group__abs(t_b)
% 0.19/0.40 = { by axiom 8 (clsrel_Ring__and__Field_Oordered__idom_50) R->L }
% 0.19/0.40 fresh2(class_Ring__and__Field_Oordered__idom(t_b), true2, t_b)
% 0.19/0.40 = { by axiom 1 (tfree_tcs) }
% 0.19/0.40 fresh2(true2, true2, t_b)
% 0.19/0.40 = { by axiom 3 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 0.19/0.40 true2
% 0.19/0.40
% 0.19/0.40 Goal 1 (cls_conjecture_2): c_lessequals(v_f(v_x(X)), c_times(X, c_HOL_Oabs(v_g(v_x(X)), t_b), t_b), t_b) = true2.
% 0.19/0.40 The goal is true when:
% 0.19/0.40 X = c_HOL_Oabs(v_c, t_b)
% 0.19/0.40
% 0.19/0.40 Proof:
% 0.19/0.40 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), t_b)
% 0.19/0.40 = { by axiom 12 (cls_Ring__and__Field_Oabs__mult_0) R->L }
% 0.19/0.40 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh4(class_Ring__and__Field_Oordered__idom(t_b), true2, t_b, v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b)))), t_b)
% 0.19/0.40 = { by axiom 1 (tfree_tcs) }
% 0.19/0.40 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh4(true2, true2, t_b, v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b)))), t_b)
% 0.19/0.40 = { by axiom 10 (cls_Ring__and__Field_Oabs__mult_0) }
% 0.19/0.40 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_HOL_Oabs(c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), t_b)
% 0.19/0.40 = { by axiom 6 (cls_OrderedGroup_Oabs__of__nonneg_0) R->L }
% 0.19/0.40 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh5(true2, true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.19/0.40 = { by axiom 9 (cls_Orderings_Oorder__class_Oorder__trans_0) R->L }
% 0.19/0.40 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh5(fresh8(true2, true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), c_0), true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.19/0.40 = { by axiom 14 (cls_conjecture_1) R->L }
% 0.19/0.40 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh5(fresh8(c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), c_0), true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.19/0.41 = { by axiom 15 (cls_Orderings_Oorder__class_Oorder__trans_0) R->L }
% 0.19/0.41 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh5(fresh7(true2, true2, t_b, v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), c_0), true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.19/0.41 = { by axiom 2 (clsrel_OrderedGroup_Olordered__ab__group__abs_17) R->L }
% 0.19/0.41 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh5(fresh7(fresh3(true2, true2, t_b), true2, t_b, v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), c_0), true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.19/0.41 = { by lemma 17 R->L }
% 0.19/0.41 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh5(fresh7(fresh3(class_OrderedGroup_Olordered__ab__group__abs(t_b), true2, t_b), true2, t_b, v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), c_0), true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.19/0.41 = { by axiom 7 (clsrel_OrderedGroup_Olordered__ab__group__abs_17) }
% 0.19/0.41 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh5(fresh7(class_Orderings_Oorder(t_b), true2, t_b, v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), c_0), true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.19/0.41 = { by axiom 16 (cls_Orderings_Oorder__class_Oorder__trans_0) }
% 0.19/0.41 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh5(fresh6(c_lessequals(c_0, v_f(v_x(c_HOL_Oabs(v_c, t_b))), t_b), true2, t_b, v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), c_0), true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.19/0.41 = { by axiom 4 (cls_conjecture_0) }
% 0.19/0.41 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh5(fresh6(true2, true2, t_b, v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), c_0), true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.19/0.41 = { by axiom 11 (cls_Orderings_Oorder__class_Oorder__trans_0) }
% 0.19/0.41 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh5(c_lessequals(c_0, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b), true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.19/0.41 = { by axiom 13 (cls_OrderedGroup_Oabs__of__nonneg_0) }
% 0.19/0.41 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh(class_OrderedGroup_Olordered__ab__group__abs(t_b), true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.19/0.41 = { by lemma 17 }
% 0.19/0.41 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), fresh(true2, true2, t_b, c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b)), t_b)
% 0.19/0.41 = { by axiom 5 (cls_OrderedGroup_Oabs__of__nonneg_0) }
% 0.19/0.41 c_lessequals(v_f(v_x(c_HOL_Oabs(v_c, t_b))), c_times(v_c, v_g(v_x(c_HOL_Oabs(v_c, t_b))), t_b), t_b)
% 0.19/0.41 = { by axiom 14 (cls_conjecture_1) }
% 0.19/0.41 true2
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
% 0.19/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------