TSTP Solution File: ANA039-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA039-2 : 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 : n024.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 17:21:11 EDT 2023
% Result : Unsatisfiable 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA039-2 : 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
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % 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 18:40:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.43 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.43
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.43
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 Take the following subset of the input axioms:
% 0.21/0.45 fof(cls_OrderedGroup_Oabs__ge__self_0, axiom, ![T_a, V_a]: (~class_OrderedGroup_Olordered__ab__group__abs(T_a) | c_lessequals(V_a, c_HOL_Oabs(V_a, T_a), T_a))).
% 0.21/0.45 fof(cls_OrderedGroup_Oabs__ge__zero_0, axiom, ![T_a2, V_a2]: (~class_OrderedGroup_Olordered__ab__group__abs(T_a2) | c_lessequals(c_0, c_HOL_Oabs(V_a2, T_a2), T_a2))).
% 0.21/0.45 fof(cls_Orderings_Oorder__class_Oorder__trans_0, axiom, ![V_y, V_z, V_x, T_a2]: (~class_Orderings_Oorder(T_a2) | (~c_lessequals(V_y, V_z, T_a2) | (~c_lessequals(V_x, V_y, T_a2) | c_lessequals(V_x, V_z, T_a2))))).
% 0.21/0.45 fof(cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0, axiom, ![V_b, V_c, T_a2, V_a2]: (~class_Ring__and__Field_Opordered__semiring(T_a2) | (~c_lessequals(V_a2, V_b, T_a2) | (~c_lessequals(c_0, V_c, T_a2) | c_lessequals(c_times(V_a2, V_c, T_a2), c_times(V_b, V_c, T_a2), T_a2))))).
% 0.21/0.45 fof(cls_conjecture_0, negated_conjecture, ![V_U]: c_lessequals(c_HOL_Oabs(v_h(V_U), t_a), c_times(v_c, c_HOL_Oabs(v_f(V_U), t_a), t_a), t_a)).
% 0.21/0.45 fof(cls_conjecture_2, negated_conjecture, ~c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a)).
% 0.21/0.45 fof(clsrel_Ring__and__Field_Oordered__idom_42, axiom, ![T]: (~class_Ring__and__Field_Oordered__idom(T) | class_Ring__and__Field_Opordered__semiring(T))).
% 0.21/0.45 fof(clsrel_Ring__and__Field_Oordered__idom_44, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_Orderings_Oorder(T2))).
% 0.21/0.45 fof(clsrel_Ring__and__Field_Oordered__idom_50, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_OrderedGroup_Olordered__ab__group__abs(T2))).
% 0.21/0.45 fof(tfree_tcs, negated_conjecture, class_Ring__and__Field_Oordered__idom(t_a)).
% 0.21/0.45
% 0.21/0.45 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.45 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.45 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.45 fresh(y, y, x1...xn) = u
% 0.21/0.45 C => fresh(s, t, x1...xn) = v
% 0.21/0.45 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.45 variables of u and v.
% 0.21/0.45 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.45 input problem has no model of domain size 1).
% 0.21/0.45
% 0.21/0.45 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.45
% 0.21/0.45 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_a) = true.
% 0.21/0.45 Axiom 2 (clsrel_Ring__and__Field_Oordered__idom_50): fresh(X, X, Y) = true.
% 0.21/0.45 Axiom 3 (clsrel_Ring__and__Field_Oordered__idom_42): fresh3(X, X, Y) = true.
% 0.21/0.45 Axiom 4 (clsrel_Ring__and__Field_Oordered__idom_44): fresh2(X, X, Y) = true.
% 0.21/0.45 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_50): fresh(class_Ring__and__Field_Oordered__idom(X), true, X) = class_OrderedGroup_Olordered__ab__group__abs(X).
% 0.21/0.45 Axiom 6 (cls_OrderedGroup_Oabs__ge__zero_0): fresh7(X, X, Y, Z) = true.
% 0.21/0.45 Axiom 7 (cls_OrderedGroup_Oabs__ge__self_0): fresh6(X, X, Y, Z) = true.
% 0.21/0.45 Axiom 8 (clsrel_Ring__and__Field_Oordered__idom_42): fresh3(class_Ring__and__Field_Oordered__idom(X), true, X) = class_Ring__and__Field_Opordered__semiring(X).
% 0.21/0.45 Axiom 9 (clsrel_Ring__and__Field_Oordered__idom_44): fresh2(class_Ring__and__Field_Oordered__idom(X), true, X) = class_Orderings_Oorder(X).
% 0.21/0.45 Axiom 10 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh11(X, X, Y, Z, W) = true.
% 0.21/0.45 Axiom 11 (cls_OrderedGroup_Oabs__ge__zero_0): fresh7(class_OrderedGroup_Olordered__ab__group__abs(X), true, X, Y) = c_lessequals(c_0, c_HOL_Oabs(Y, X), X).
% 0.21/0.45 Axiom 12 (cls_OrderedGroup_Oabs__ge__self_0): fresh6(class_OrderedGroup_Olordered__ab__group__abs(X), true, X, Y) = c_lessequals(Y, c_HOL_Oabs(Y, X), X).
% 0.21/0.45 Axiom 13 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0): fresh9(X, X, Y, Z, W, V) = true.
% 0.21/0.45 Axiom 14 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh5(X, X, Y, Z, W, V) = c_lessequals(V, W, Y).
% 0.21/0.45 Axiom 15 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh10(X, X, Y, Z, W, V) = fresh11(c_lessequals(Z, W, Y), true, Y, W, V).
% 0.21/0.45 Axiom 16 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0): fresh4(X, X, Y, Z, W, V) = c_lessequals(c_times(Z, W, Y), c_times(V, W, Y), Y).
% 0.21/0.45 Axiom 17 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0): fresh8(X, X, Y, Z, W, V) = fresh9(c_lessequals(Z, V, Y), true, Y, Z, W, V).
% 0.21/0.45 Axiom 18 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh10(class_Orderings_Oorder(X), true, X, Y, Z, W) = fresh5(c_lessequals(W, Y, X), true, X, Y, Z, W).
% 0.21/0.45 Axiom 19 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0): fresh8(class_Ring__and__Field_Opordered__semiring(X), true, X, Y, Z, W) = fresh4(c_lessequals(c_0, Z, X), true, X, Y, Z, W).
% 0.21/0.45 Axiom 20 (cls_conjecture_0): c_lessequals(c_HOL_Oabs(v_h(X), t_a), c_times(v_c, c_HOL_Oabs(v_f(X), t_a), t_a), t_a) = true.
% 0.21/0.45
% 0.21/0.45 Lemma 21: class_OrderedGroup_Olordered__ab__group__abs(t_a) = true.
% 0.21/0.45 Proof:
% 0.21/0.45 class_OrderedGroup_Olordered__ab__group__abs(t_a)
% 0.21/0.45 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_50) R->L }
% 0.21/0.45 fresh(class_Ring__and__Field_Oordered__idom(t_a), true, t_a)
% 0.21/0.45 = { by axiom 1 (tfree_tcs) }
% 0.21/0.45 fresh(true, true, t_a)
% 0.21/0.45 = { by axiom 2 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 0.21/0.45 true
% 0.21/0.45
% 0.21/0.45 Goal 1 (cls_conjecture_2): c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a) = true.
% 0.21/0.45 Proof:
% 0.21/0.45 c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a)
% 0.21/0.45 = { by axiom 14 (cls_Orderings_Oorder__class_Oorder__trans_0) R->L }
% 0.21/0.45 fresh5(true, true, t_a, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.45 = { by axiom 20 (cls_conjecture_0) R->L }
% 0.21/0.45 fresh5(c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, t_a, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.45 = { by axiom 18 (cls_Orderings_Oorder__class_Oorder__trans_0) R->L }
% 0.21/0.45 fresh10(class_Orderings_Oorder(t_a), true, t_a, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.45 = { by axiom 9 (clsrel_Ring__and__Field_Oordered__idom_44) R->L }
% 0.21/0.45 fresh10(fresh2(class_Ring__and__Field_Oordered__idom(t_a), true, t_a), true, t_a, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.45 = { by axiom 1 (tfree_tcs) }
% 0.21/0.45 fresh10(fresh2(true, true, t_a), true, t_a, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.45 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_44) }
% 0.21/0.45 fresh10(true, true, t_a, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.45 = { by axiom 15 (cls_Orderings_Oorder__class_Oorder__trans_0) }
% 0.21/0.45 fresh11(c_lessequals(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_a), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a), true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.45 = { by axiom 16 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) R->L }
% 0.21/0.45 fresh11(fresh4(true, true, t_a, v_c, c_HOL_Oabs(v_f(v_x), t_a), c_HOL_Oabs(v_c, t_a)), true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.45 = { by axiom 6 (cls_OrderedGroup_Oabs__ge__zero_0) R->L }
% 0.21/0.45 fresh11(fresh4(fresh7(true, true, t_a, v_f(v_x)), true, t_a, v_c, c_HOL_Oabs(v_f(v_x), t_a), c_HOL_Oabs(v_c, t_a)), true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.45 = { by lemma 21 R->L }
% 0.21/0.45 fresh11(fresh4(fresh7(class_OrderedGroup_Olordered__ab__group__abs(t_a), true, t_a, v_f(v_x)), true, t_a, v_c, c_HOL_Oabs(v_f(v_x), t_a), c_HOL_Oabs(v_c, t_a)), true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.45 = { by axiom 11 (cls_OrderedGroup_Oabs__ge__zero_0) }
% 0.21/0.45 fresh11(fresh4(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_a), t_a), true, t_a, v_c, c_HOL_Oabs(v_f(v_x), t_a), c_HOL_Oabs(v_c, t_a)), true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.45 = { by axiom 19 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) R->L }
% 0.21/0.45 fresh11(fresh8(class_Ring__and__Field_Opordered__semiring(t_a), true, t_a, v_c, c_HOL_Oabs(v_f(v_x), t_a), c_HOL_Oabs(v_c, t_a)), true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.45 = { by axiom 8 (clsrel_Ring__and__Field_Oordered__idom_42) R->L }
% 0.21/0.46 fresh11(fresh8(fresh3(class_Ring__and__Field_Oordered__idom(t_a), true, t_a), true, t_a, v_c, c_HOL_Oabs(v_f(v_x), t_a), c_HOL_Oabs(v_c, t_a)), true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.46 = { by axiom 1 (tfree_tcs) }
% 0.21/0.46 fresh11(fresh8(fresh3(true, true, t_a), true, t_a, v_c, c_HOL_Oabs(v_f(v_x), t_a), c_HOL_Oabs(v_c, t_a)), true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.46 = { by axiom 3 (clsrel_Ring__and__Field_Oordered__idom_42) }
% 0.21/0.46 fresh11(fresh8(true, true, t_a, v_c, c_HOL_Oabs(v_f(v_x), t_a), c_HOL_Oabs(v_c, t_a)), true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.46 = { by axiom 17 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) }
% 0.21/0.46 fresh11(fresh9(c_lessequals(v_c, c_HOL_Oabs(v_c, t_a), t_a), true, t_a, v_c, c_HOL_Oabs(v_f(v_x), t_a), c_HOL_Oabs(v_c, t_a)), true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.46 = { by axiom 12 (cls_OrderedGroup_Oabs__ge__self_0) R->L }
% 0.21/0.46 fresh11(fresh9(fresh6(class_OrderedGroup_Olordered__ab__group__abs(t_a), true, t_a, v_c), true, t_a, v_c, c_HOL_Oabs(v_f(v_x), t_a), c_HOL_Oabs(v_c, t_a)), true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.46 = { by lemma 21 }
% 0.21/0.46 fresh11(fresh9(fresh6(true, true, t_a, v_c), true, t_a, v_c, c_HOL_Oabs(v_f(v_x), t_a), c_HOL_Oabs(v_c, t_a)), true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.46 = { by axiom 7 (cls_OrderedGroup_Oabs__ge__self_0) }
% 0.21/0.46 fresh11(fresh9(true, true, t_a, v_c, c_HOL_Oabs(v_f(v_x), t_a), c_HOL_Oabs(v_c, t_a)), true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.46 = { by axiom 13 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) }
% 0.21/0.46 fresh11(true, true, t_a, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), c_HOL_Oabs(v_h(v_x), t_a))
% 0.21/0.46 = { by axiom 10 (cls_Orderings_Oorder__class_Oorder__trans_0) }
% 0.21/0.46 true
% 0.21/0.46 % SZS output end Proof
% 0.21/0.46
% 0.21/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------