TSTP Solution File: ANA024-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA024-2 : 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 : n028.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 17:21:06 EDT 2023
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA024-2 : 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
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 18:42:36 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.40 Command-line arguments: --flatten
% 0.21/0.40
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 Take the following subset of the input axioms:
% 0.21/0.41 fof(cls_OrderedGroup_Ocompare__rls__10_0, axiom, ![T_a, V_a, V_b]: (~class_OrderedGroup_Oab__group__add(T_a) | V_a=c_plus(c_minus(V_a, V_b, T_a), V_b, T_a))).
% 0.21/0.41 fof(cls_OrderedGroup_Ocompare__rls__9_1, axiom, ![V_c, T_a2, V_a2, V_b2]: (~class_OrderedGroup_Opordered__ab__group__add(T_a2) | (~c_lessequals(c_plus(V_a2, V_b2, T_a2), V_c, T_a2) | c_lessequals(V_a2, c_minus(V_c, V_b2, T_a2), T_a2)))).
% 0.21/0.41 fof(cls_conjecture_1, negated_conjecture, ![V_U]: c_lessequals(v_k(V_U), v_f(V_U), t_b)).
% 0.21/0.41 fof(cls_conjecture_3, negated_conjecture, ~c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)).
% 0.21/0.41 fof(clsrel_OrderedGroup_Opordered__ab__group__add_0, axiom, ![T]: (~class_OrderedGroup_Opordered__ab__group__add(T) | class_OrderedGroup_Oab__group__add(T))).
% 0.21/0.41 fof(clsrel_Ring__and__Field_Oordered__idom_54, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_OrderedGroup_Opordered__ab__group__add(T2))).
% 0.21/0.41 fof(tfree_tcs, negated_conjecture, class_Ring__and__Field_Oordered__idom(t_b)).
% 0.21/0.41
% 0.21/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.41 fresh(y, y, x1...xn) = u
% 0.21/0.41 C => fresh(s, t, x1...xn) = v
% 0.21/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.41 variables of u and v.
% 0.21/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.41 input problem has no model of domain size 1).
% 0.21/0.41
% 0.21/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.41
% 0.21/0.41 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.21/0.41 Axiom 2 (clsrel_OrderedGroup_Opordered__ab__group__add_0): fresh3(X, X, Y) = true.
% 0.21/0.41 Axiom 3 (clsrel_Ring__and__Field_Oordered__idom_54): fresh2(X, X, Y) = true.
% 0.21/0.41 Axiom 4 (clsrel_OrderedGroup_Opordered__ab__group__add_0): fresh3(class_OrderedGroup_Opordered__ab__group__add(X), true, X) = class_OrderedGroup_Oab__group__add(X).
% 0.21/0.41 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_54): fresh2(class_Ring__and__Field_Oordered__idom(X), true, X) = class_OrderedGroup_Opordered__ab__group__add(X).
% 0.21/0.41 Axiom 6 (cls_OrderedGroup_Ocompare__rls__10_0): fresh(X, X, Y, Z, W) = Z.
% 0.21/0.41 Axiom 7 (cls_conjecture_1): c_lessequals(v_k(X), v_f(X), t_b) = true.
% 0.21/0.41 Axiom 8 (cls_OrderedGroup_Ocompare__rls__10_0): fresh(class_OrderedGroup_Oab__group__add(X), true, X, Y, Z) = c_plus(c_minus(Y, Z, X), Z, X).
% 0.21/0.41 Axiom 9 (cls_OrderedGroup_Ocompare__rls__9_1): fresh5(X, X, Y, Z, W, V) = true.
% 0.21/0.41 Axiom 10 (cls_OrderedGroup_Ocompare__rls__9_1): fresh4(X, X, Y, Z, W, V) = c_lessequals(Z, c_minus(V, W, Y), Y).
% 0.21/0.41 Axiom 11 (cls_OrderedGroup_Ocompare__rls__9_1): fresh4(c_lessequals(c_plus(X, Y, Z), W, Z), true, Z, X, Y, W) = fresh5(class_OrderedGroup_Opordered__ab__group__add(Z), true, Z, X, Y, W).
% 0.21/0.41
% 0.21/0.41 Lemma 12: class_Ring__and__Field_Oordered__idom(t_b) = class_OrderedGroup_Opordered__ab__group__add(t_b).
% 0.21/0.41 Proof:
% 0.21/0.41 class_Ring__and__Field_Oordered__idom(t_b)
% 0.21/0.41 = { by axiom 1 (tfree_tcs) }
% 0.21/0.41 true
% 0.21/0.41 = { by axiom 3 (clsrel_Ring__and__Field_Oordered__idom_54) R->L }
% 0.21/0.41 fresh2(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b)
% 0.21/0.41 = { by axiom 1 (tfree_tcs) }
% 0.21/0.41 fresh2(class_Ring__and__Field_Oordered__idom(t_b), true, t_b)
% 0.21/0.41 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_54) }
% 0.21/0.41 class_OrderedGroup_Opordered__ab__group__add(t_b)
% 0.21/0.41
% 0.21/0.41 Goal 1 (cls_conjecture_3): c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = true.
% 0.21/0.41 Proof:
% 0.21/0.41 c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 0.21/0.41 = { by axiom 10 (cls_OrderedGroup_Ocompare__rls__9_1) R->L }
% 0.21/0.41 fresh4(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by axiom 1 (tfree_tcs) }
% 0.21/0.41 fresh4(true, class_Ring__and__Field_Oordered__idom(t_b), t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by axiom 7 (cls_conjecture_1) R->L }
% 0.21/0.41 fresh4(c_lessequals(v_k(v_x), v_f(v_x), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by axiom 6 (cls_OrderedGroup_Ocompare__rls__10_0) R->L }
% 0.21/0.41 fresh4(c_lessequals(fresh(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, v_k(v_x), v_g(v_x)), v_f(v_x), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by axiom 1 (tfree_tcs) }
% 0.21/0.41 fresh4(c_lessequals(fresh(true, class_Ring__and__Field_Oordered__idom(t_b), t_b, v_k(v_x), v_g(v_x)), v_f(v_x), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by axiom 2 (clsrel_OrderedGroup_Opordered__ab__group__add_0) R->L }
% 0.21/0.41 fresh4(c_lessequals(fresh(fresh3(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, v_k(v_x), v_g(v_x)), v_f(v_x), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by lemma 12 }
% 0.21/0.41 fresh4(c_lessequals(fresh(fresh3(class_OrderedGroup_Opordered__ab__group__add(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, v_k(v_x), v_g(v_x)), v_f(v_x), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by axiom 1 (tfree_tcs) }
% 0.21/0.41 fresh4(c_lessequals(fresh(fresh3(class_OrderedGroup_Opordered__ab__group__add(t_b), true, t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, v_k(v_x), v_g(v_x)), v_f(v_x), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by axiom 4 (clsrel_OrderedGroup_Opordered__ab__group__add_0) }
% 0.21/0.41 fresh4(c_lessequals(fresh(class_OrderedGroup_Oab__group__add(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, v_k(v_x), v_g(v_x)), v_f(v_x), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by axiom 1 (tfree_tcs) }
% 0.21/0.41 fresh4(c_lessequals(fresh(class_OrderedGroup_Oab__group__add(t_b), true, t_b, v_k(v_x), v_g(v_x)), v_f(v_x), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by axiom 8 (cls_OrderedGroup_Ocompare__rls__10_0) }
% 0.21/0.41 fresh4(c_lessequals(c_plus(c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by axiom 1 (tfree_tcs) }
% 0.21/0.41 fresh4(c_lessequals(c_plus(c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), t_b), v_f(v_x), t_b), true, t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by axiom 11 (cls_OrderedGroup_Ocompare__rls__9_1) }
% 0.21/0.41 fresh5(class_OrderedGroup_Opordered__ab__group__add(t_b), true, t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by axiom 1 (tfree_tcs) R->L }
% 0.21/0.41 fresh5(class_OrderedGroup_Opordered__ab__group__add(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by lemma 12 R->L }
% 0.21/0.41 fresh5(class_Ring__and__Field_Oordered__idom(t_b), class_Ring__and__Field_Oordered__idom(t_b), t_b, c_minus(v_k(v_x), v_g(v_x), t_b), v_g(v_x), v_f(v_x))
% 0.21/0.41 = { by axiom 9 (cls_OrderedGroup_Ocompare__rls__9_1) }
% 0.21/0.41 true
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41
% 0.21/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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