TSTP Solution File: ANA009-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA009-2 : 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 : n001.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 0.38s
% Output : Proof 0.19s
% 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 : ANA009-2 : 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
% 0.15/0.33 % Computer : n001.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Fri Aug 25 18:55:44 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.38 Command-line arguments: --no-flatten-goal
% 0.19/0.38
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 Take the following subset of the input axioms:
% 0.19/0.38 fof(cls_OrderedGroup_Oadd__le__cancel__right_1, axiom, ![T_a, V_a, V_b, V_c]: (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | (~c_lessequals(V_a, V_b, T_a) | c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a)))).
% 0.19/0.38 fof(cls_OrderedGroup_Oright__minus_0, axiom, ![T_a2, V_a2]: (~class_OrderedGroup_Oab__group__add(T_a2) | c_plus(V_a2, c_uminus(V_a2, T_a2), T_a2)=c_0)).
% 0.19/0.38 fof(cls_conjecture_0, negated_conjecture, ![V_U]: c_lessequals(v_lb(V_U), v_f(V_U), t_b)).
% 0.19/0.38 fof(cls_conjecture_2, negated_conjecture, ~c_lessequals(c_0, c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)).
% 0.19/0.38 fof(clsrel_Ring__and__Field_Oordered__idom_37, axiom, ![T]: (~class_Ring__and__Field_Oordered__idom(T) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T))).
% 0.19/0.38 fof(clsrel_Ring__and__Field_Oordered__idom_4, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_OrderedGroup_Oab__group__add(T2))).
% 0.19/0.38 fof(tfree_tcs, negated_conjecture, class_Ring__and__Field_Oordered__idom(t_b)).
% 0.19/0.38
% 0.19/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.38 fresh(y, y, x1...xn) = u
% 0.19/0.38 C => fresh(s, t, x1...xn) = v
% 0.19/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.38 variables of u and v.
% 0.19/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.38 input problem has no model of domain size 1).
% 0.19/0.38
% 0.19/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.38
% 0.19/0.38 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.19/0.38 Axiom 2 (clsrel_Ring__and__Field_Oordered__idom_4): fresh(X, X, Y) = true.
% 0.19/0.38 Axiom 3 (clsrel_Ring__and__Field_Oordered__idom_37): fresh2(X, X, Y) = true.
% 0.19/0.38 Axiom 4 (clsrel_Ring__and__Field_Oordered__idom_4): fresh(class_Ring__and__Field_Oordered__idom(X), true, X) = class_OrderedGroup_Oab__group__add(X).
% 0.19/0.38 Axiom 5 (cls_OrderedGroup_Oright__minus_0): fresh3(X, X, Y, Z) = c_0.
% 0.19/0.38 Axiom 6 (clsrel_Ring__and__Field_Oordered__idom_37): fresh2(class_Ring__and__Field_Oordered__idom(X), true, X) = class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X).
% 0.19/0.38 Axiom 7 (cls_conjecture_0): c_lessequals(v_lb(X), v_f(X), t_b) = true.
% 0.19/0.38 Axiom 8 (cls_OrderedGroup_Oright__minus_0): fresh3(class_OrderedGroup_Oab__group__add(X), true, X, Y) = c_plus(Y, c_uminus(Y, X), X).
% 0.19/0.38 Axiom 9 (cls_OrderedGroup_Oadd__le__cancel__right_1): fresh5(X, X, Y, Z, W, V) = true.
% 0.19/0.38 Axiom 10 (cls_OrderedGroup_Oadd__le__cancel__right_1): fresh4(X, X, Y, Z, W, V) = fresh5(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(Y), true, Y, Z, W, V).
% 0.19/0.38 Axiom 11 (cls_OrderedGroup_Oadd__le__cancel__right_1): fresh4(c_lessequals(X, Y, Z), true, Z, X, Y, W) = c_lessequals(c_plus(X, W, Z), c_plus(Y, W, Z), Z).
% 0.19/0.38
% 0.19/0.38 Goal 1 (cls_conjecture_2): c_lessequals(c_0, c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b) = true.
% 0.19/0.38 Proof:
% 0.19/0.38 c_lessequals(c_0, c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)
% 0.19/0.38 = { by axiom 5 (cls_OrderedGroup_Oright__minus_0) R->L }
% 0.19/0.38 c_lessequals(fresh3(true, true, t_b, v_lb(v_x)), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)
% 0.19/0.38 = { by axiom 2 (clsrel_Ring__and__Field_Oordered__idom_4) R->L }
% 0.19/0.38 c_lessequals(fresh3(fresh(true, true, t_b), true, t_b, v_lb(v_x)), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)
% 0.19/0.38 = { by axiom 1 (tfree_tcs) R->L }
% 0.19/0.38 c_lessequals(fresh3(fresh(class_Ring__and__Field_Oordered__idom(t_b), true, t_b), true, t_b, v_lb(v_x)), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)
% 0.19/0.39 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_4) }
% 0.19/0.39 c_lessequals(fresh3(class_OrderedGroup_Oab__group__add(t_b), true, t_b, v_lb(v_x)), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)
% 0.19/0.39 = { by axiom 8 (cls_OrderedGroup_Oright__minus_0) }
% 0.19/0.39 c_lessequals(c_plus(v_lb(v_x), c_uminus(v_lb(v_x), t_b), t_b), c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)
% 0.19/0.39 = { by axiom 11 (cls_OrderedGroup_Oadd__le__cancel__right_1) R->L }
% 0.19/0.39 fresh4(c_lessequals(v_lb(v_x), v_f(v_x), t_b), true, t_b, v_lb(v_x), v_f(v_x), c_uminus(v_lb(v_x), t_b))
% 0.19/0.39 = { by axiom 7 (cls_conjecture_0) }
% 0.19/0.39 fresh4(true, true, t_b, v_lb(v_x), v_f(v_x), c_uminus(v_lb(v_x), t_b))
% 0.19/0.39 = { by axiom 10 (cls_OrderedGroup_Oadd__le__cancel__right_1) }
% 0.19/0.39 fresh5(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b), true, t_b, v_lb(v_x), v_f(v_x), c_uminus(v_lb(v_x), t_b))
% 0.19/0.39 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_37) R->L }
% 0.19/0.39 fresh5(fresh2(class_Ring__and__Field_Oordered__idom(t_b), true, t_b), true, t_b, v_lb(v_x), v_f(v_x), c_uminus(v_lb(v_x), t_b))
% 0.19/0.39 = { by axiom 1 (tfree_tcs) }
% 0.19/0.39 fresh5(fresh2(true, true, t_b), true, t_b, v_lb(v_x), v_f(v_x), c_uminus(v_lb(v_x), t_b))
% 0.19/0.39 = { by axiom 3 (clsrel_Ring__and__Field_Oordered__idom_37) }
% 0.19/0.39 fresh5(true, true, t_b, v_lb(v_x), v_f(v_x), c_uminus(v_lb(v_x), t_b))
% 0.19/0.39 = { by axiom 9 (cls_OrderedGroup_Oadd__le__cancel__right_1) }
% 0.19/0.39 true
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
% 0.19/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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