TSTP Solution File: ANA027-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA027-2 : 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 : n020.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 17:21:07 EDT 2023
% Result : Unsatisfiable 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : ANA027-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % 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 : n020.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 18:50:30 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.42 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.42
% 0.21/0.42 % SZS status Unsatisfiable
% 0.21/0.42
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 Take the following subset of the input axioms:
% 0.21/0.44 fof(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0, axiom, ![T_a, V_y]: (~class_OrderedGroup_Ocomm__monoid__add(T_a) | c_plus(c_0, V_y, T_a)=V_y)).
% 0.21/0.44 fof(cls_OrderedGroup_Ocompare__rls__9_0, axiom, ![V_a, V_c, V_b, T_a2]: (~class_OrderedGroup_Opordered__ab__group__add(T_a2) | (~c_lessequals(V_a, c_minus(V_c, V_b, T_a2), T_a2) | c_lessequals(c_plus(V_a, V_b, T_a2), V_c, T_a2)))).
% 0.21/0.44 fof(cls_OrderedGroup_Ocompare__rls__9_1, axiom, ![T_a2, V_a2, V_c2, V_b2]: (~class_OrderedGroup_Opordered__ab__group__add(T_a2) | (~c_lessequals(c_plus(V_a2, V_b2, T_a2), V_c2, T_a2) | c_lessequals(V_a2, c_minus(V_c2, V_b2, T_a2), T_a2)))).
% 0.21/0.44 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))))).
% 0.21/0.44 fof(cls_conjecture_1, negated_conjecture, c_lessequals(c_0, c_minus(v_f(v_x), v_k(v_x), t_b), t_b)).
% 0.21/0.44 fof(cls_conjecture_2, negated_conjecture, c_lessequals(v_g(v_x), v_k(v_x), t_b)).
% 0.21/0.44 fof(cls_conjecture_3, negated_conjecture, ~c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b)).
% 0.21/0.44 fof(clsrel_LOrder_Ojoin__semilorder_1, axiom, ![T]: (~class_LOrder_Ojoin__semilorder(T) | class_Orderings_Oorder(T))).
% 0.21/0.44 fof(clsrel_OrderedGroup_Olordered__ab__group__abs_1, axiom, ![T2]: (~class_OrderedGroup_Olordered__ab__group__abs(T2) | class_OrderedGroup_Opordered__ab__group__add(T2))).
% 0.21/0.44 fof(clsrel_OrderedGroup_Olordered__ab__group__abs_15, axiom, ![T2]: (~class_OrderedGroup_Olordered__ab__group__abs(T2) | class_LOrder_Ojoin__semilorder(T2))).
% 0.21/0.44 fof(clsrel_Ring__and__Field_Oordered__idom_23, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_OrderedGroup_Ocomm__monoid__add(T2))).
% 0.21/0.44 fof(clsrel_Ring__and__Field_Oordered__idom_50, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_OrderedGroup_Olordered__ab__group__abs(T2))).
% 0.21/0.44 fof(tfree_tcs, negated_conjecture, class_Ring__and__Field_Oordered__idom(t_b)).
% 0.21/0.44
% 0.21/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.44 fresh(y, y, x1...xn) = u
% 0.21/0.44 C => fresh(s, t, x1...xn) = v
% 0.21/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.44 variables of u and v.
% 0.21/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.44 input problem has no model of domain size 1).
% 0.21/0.44
% 0.21/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.44
% 0.21/0.44 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.21/0.44 Axiom 2 (clsrel_LOrder_Ojoin__semilorder_1): fresh6(X, X, Y) = true.
% 0.21/0.44 Axiom 3 (clsrel_OrderedGroup_Olordered__ab__group__abs_1): fresh5(X, X, Y) = true.
% 0.21/0.44 Axiom 4 (clsrel_OrderedGroup_Olordered__ab__group__abs_15): fresh4(X, X, Y) = true.
% 0.21/0.44 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_23): fresh3(X, X, Y) = true.
% 0.21/0.44 Axiom 6 (clsrel_Ring__and__Field_Oordered__idom_50): fresh2(X, X, Y) = true.
% 0.21/0.44 Axiom 7 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0): fresh(X, X, Y, Z) = Z.
% 0.21/0.44 Axiom 8 (clsrel_LOrder_Ojoin__semilorder_1): fresh6(class_LOrder_Ojoin__semilorder(X), true, X) = class_Orderings_Oorder(X).
% 0.21/0.44 Axiom 9 (clsrel_OrderedGroup_Olordered__ab__group__abs_1): fresh5(class_OrderedGroup_Olordered__ab__group__abs(X), true, X) = class_OrderedGroup_Opordered__ab__group__add(X).
% 0.21/0.44 Axiom 10 (clsrel_OrderedGroup_Olordered__ab__group__abs_15): fresh4(class_OrderedGroup_Olordered__ab__group__abs(X), true, X) = class_LOrder_Ojoin__semilorder(X).
% 0.21/0.44 Axiom 11 (clsrel_Ring__and__Field_Oordered__idom_23): fresh3(class_Ring__and__Field_Oordered__idom(X), true, X) = class_OrderedGroup_Ocomm__monoid__add(X).
% 0.21/0.44 Axiom 12 (clsrel_Ring__and__Field_Oordered__idom_50): fresh2(class_Ring__and__Field_Oordered__idom(X), true, X) = class_OrderedGroup_Olordered__ab__group__abs(X).
% 0.21/0.44 Axiom 13 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0): fresh(class_OrderedGroup_Ocomm__monoid__add(X), true, X, Y) = c_plus(c_0, Y, X).
% 0.21/0.44 Axiom 14 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh13(X, X, Y, Z, W) = true.
% 0.21/0.44 Axiom 15 (cls_conjecture_2): c_lessequals(v_g(v_x), v_k(v_x), t_b) = true.
% 0.21/0.44 Axiom 16 (cls_OrderedGroup_Ocompare__rls__9_0): fresh11(X, X, Y, Z, W, V) = true.
% 0.21/0.44 Axiom 17 (cls_OrderedGroup_Ocompare__rls__9_1): fresh8(X, X, Y, Z, W, V) = true.
% 0.21/0.44 Axiom 18 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh7(X, X, Y, Z, W, V) = c_lessequals(V, W, Y).
% 0.21/0.44 Axiom 19 (cls_OrderedGroup_Ocompare__rls__9_1): fresh9(X, X, Y, Z, W, V) = c_lessequals(Z, c_minus(V, W, Y), Y).
% 0.21/0.44 Axiom 20 (cls_OrderedGroup_Ocompare__rls__9_0): fresh10(X, X, Y, Z, W, V) = c_lessequals(c_plus(Z, V, Y), W, Y).
% 0.21/0.44 Axiom 21 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh12(X, X, Y, Z, W, V) = fresh13(c_lessequals(Z, W, Y), true, Y, W, V).
% 0.21/0.44 Axiom 22 (cls_conjecture_1): c_lessequals(c_0, c_minus(v_f(v_x), v_k(v_x), t_b), t_b) = true.
% 0.21/0.44 Axiom 23 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh12(class_Orderings_Oorder(X), true, X, Y, Z, W) = fresh7(c_lessequals(W, Y, X), true, X, Y, Z, W).
% 0.21/0.44 Axiom 24 (cls_OrderedGroup_Ocompare__rls__9_0): fresh10(class_OrderedGroup_Opordered__ab__group__add(X), true, X, Y, Z, W) = fresh11(c_lessequals(Y, c_minus(Z, W, X), X), true, X, Y, Z, W).
% 0.21/0.44 Axiom 25 (cls_OrderedGroup_Ocompare__rls__9_1): fresh9(class_OrderedGroup_Opordered__ab__group__add(X), true, X, Y, Z, W) = fresh8(c_lessequals(c_plus(Y, Z, X), W, X), true, X, Y, Z, W).
% 0.21/0.44
% 0.21/0.44 Lemma 26: class_OrderedGroup_Olordered__ab__group__abs(t_b) = true.
% 0.21/0.44 Proof:
% 0.21/0.44 class_OrderedGroup_Olordered__ab__group__abs(t_b)
% 0.21/0.44 = { by axiom 12 (clsrel_Ring__and__Field_Oordered__idom_50) R->L }
% 0.21/0.44 fresh2(class_Ring__and__Field_Oordered__idom(t_b), true, t_b)
% 0.21/0.44 = { by axiom 1 (tfree_tcs) }
% 0.21/0.44 fresh2(true, true, t_b)
% 0.21/0.44 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 0.21/0.44 true
% 0.21/0.44
% 0.21/0.44 Lemma 27: class_OrderedGroup_Opordered__ab__group__add(t_b) = true.
% 0.21/0.44 Proof:
% 0.21/0.44 class_OrderedGroup_Opordered__ab__group__add(t_b)
% 0.21/0.44 = { by axiom 9 (clsrel_OrderedGroup_Olordered__ab__group__abs_1) R->L }
% 0.21/0.44 fresh5(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, t_b)
% 0.21/0.44 = { by lemma 26 }
% 0.21/0.44 fresh5(true, true, t_b)
% 0.21/0.44 = { by axiom 3 (clsrel_OrderedGroup_Olordered__ab__group__abs_1) }
% 0.21/0.44 true
% 0.21/0.44
% 0.21/0.44 Lemma 28: fresh10(X, X, t_b, c_0, Y, Z) = c_lessequals(Z, Y, t_b).
% 0.21/0.44 Proof:
% 0.21/0.44 fresh10(X, X, t_b, c_0, Y, Z)
% 0.21/0.44 = { by axiom 20 (cls_OrderedGroup_Ocompare__rls__9_0) }
% 0.21/0.44 c_lessequals(c_plus(c_0, Z, t_b), Y, t_b)
% 0.21/0.44 = { by axiom 13 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) R->L }
% 0.21/0.44 c_lessequals(fresh(class_OrderedGroup_Ocomm__monoid__add(t_b), true, t_b, Z), Y, t_b)
% 0.21/0.44 = { by axiom 11 (clsrel_Ring__and__Field_Oordered__idom_23) R->L }
% 0.21/0.44 c_lessequals(fresh(fresh3(class_Ring__and__Field_Oordered__idom(t_b), true, t_b), true, t_b, Z), Y, t_b)
% 0.21/0.44 = { by axiom 1 (tfree_tcs) }
% 0.21/0.44 c_lessequals(fresh(fresh3(true, true, t_b), true, t_b, Z), Y, t_b)
% 0.21/0.44 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_23) }
% 0.21/0.44 c_lessequals(fresh(true, true, t_b, Z), Y, t_b)
% 0.21/0.44 = { by axiom 7 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) }
% 0.21/0.44 c_lessequals(Z, Y, t_b)
% 0.21/0.44
% 0.21/0.44 Goal 1 (cls_conjecture_3): c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = true.
% 0.21/0.44 Proof:
% 0.21/0.44 c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 0.21/0.44 = { by axiom 19 (cls_OrderedGroup_Ocompare__rls__9_1) R->L }
% 0.21/0.44 fresh9(true, true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.44 = { by lemma 27 R->L }
% 0.21/0.44 fresh9(class_OrderedGroup_Opordered__ab__group__add(t_b), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.44 = { by axiom 25 (cls_OrderedGroup_Ocompare__rls__9_1) }
% 0.21/0.44 fresh8(c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_f(v_x), t_b), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.44 = { by axiom 20 (cls_OrderedGroup_Ocompare__rls__9_0) R->L }
% 0.21/0.44 fresh8(fresh10(X, X, t_b, c_0, v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.44 = { by lemma 28 }
% 0.21/0.44 fresh8(c_lessequals(v_g(v_x), v_f(v_x), t_b), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.44 = { by axiom 18 (cls_Orderings_Oorder__class_Oorder__trans_0) R->L }
% 0.21/0.44 fresh8(fresh7(true, true, t_b, v_k(v_x), v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.44 = { by axiom 15 (cls_conjecture_2) R->L }
% 0.21/0.45 fresh8(fresh7(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, t_b, v_k(v_x), v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by axiom 23 (cls_Orderings_Oorder__class_Oorder__trans_0) R->L }
% 0.21/0.45 fresh8(fresh12(class_Orderings_Oorder(t_b), true, t_b, v_k(v_x), v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by axiom 8 (clsrel_LOrder_Ojoin__semilorder_1) R->L }
% 0.21/0.45 fresh8(fresh12(fresh6(class_LOrder_Ojoin__semilorder(t_b), true, t_b), true, t_b, v_k(v_x), v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by axiom 10 (clsrel_OrderedGroup_Olordered__ab__group__abs_15) R->L }
% 0.21/0.45 fresh8(fresh12(fresh6(fresh4(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, t_b), true, t_b), true, t_b, v_k(v_x), v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by lemma 26 }
% 0.21/0.45 fresh8(fresh12(fresh6(fresh4(true, true, t_b), true, t_b), true, t_b, v_k(v_x), v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by axiom 4 (clsrel_OrderedGroup_Olordered__ab__group__abs_15) }
% 0.21/0.45 fresh8(fresh12(fresh6(true, true, t_b), true, t_b, v_k(v_x), v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by axiom 2 (clsrel_LOrder_Ojoin__semilorder_1) }
% 0.21/0.45 fresh8(fresh12(true, true, t_b, v_k(v_x), v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by axiom 21 (cls_Orderings_Oorder__class_Oorder__trans_0) }
% 0.21/0.45 fresh8(fresh13(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, t_b, v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by lemma 28 R->L }
% 0.21/0.45 fresh8(fresh13(fresh10(true, true, t_b, c_0, v_f(v_x), v_k(v_x)), true, t_b, v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by lemma 27 R->L }
% 0.21/0.45 fresh8(fresh13(fresh10(class_OrderedGroup_Opordered__ab__group__add(t_b), true, t_b, c_0, v_f(v_x), v_k(v_x)), true, t_b, v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by axiom 24 (cls_OrderedGroup_Ocompare__rls__9_0) }
% 0.21/0.45 fresh8(fresh13(fresh11(c_lessequals(c_0, c_minus(v_f(v_x), v_k(v_x), t_b), t_b), true, t_b, c_0, v_f(v_x), v_k(v_x)), true, t_b, v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by axiom 22 (cls_conjecture_1) }
% 0.21/0.45 fresh8(fresh13(fresh11(true, true, t_b, c_0, v_f(v_x), v_k(v_x)), true, t_b, v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by axiom 16 (cls_OrderedGroup_Ocompare__rls__9_0) }
% 0.21/0.45 fresh8(fresh13(true, true, t_b, v_f(v_x), v_g(v_x)), true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by axiom 14 (cls_Orderings_Oorder__class_Oorder__trans_0) }
% 0.21/0.45 fresh8(true, true, t_b, c_0, v_g(v_x), v_f(v_x))
% 0.21/0.45 = { by axiom 17 (cls_OrderedGroup_Ocompare__rls__9_1) }
% 0.21/0.45 true
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45
% 0.21/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------