TSTP Solution File: ANA038-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA038-2 : 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 : n032.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 0.10s 0.34s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ANA038-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Fri Aug 25 18:35:58 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.10/0.34 Command-line arguments: --ground-connectedness --complete-subsets
% 0.10/0.34
% 0.10/0.34 % SZS status Unsatisfiable
% 0.10/0.34
% 0.10/0.34 % SZS output start Proof
% 0.10/0.34 Take the following subset of the input axioms:
% 0.10/0.34 fof(cls_Orderings_Ole__maxI2_0, axiom, ![T_b, V_y, V_x]: (~class_Orderings_Olinorder(T_b) | c_lessequals(V_y, c_Orderings_Omax(V_x, V_y, T_b), T_b))).
% 0.10/0.34 fof(cls_Orderings_Oorder__class_Oorder__trans_0, axiom, ![T_a, V_z, V_y2, V_x2]: (~class_Orderings_Oorder(T_a) | (~c_lessequals(V_y2, V_z, T_a) | (~c_lessequals(V_x2, V_y2, T_a) | c_lessequals(V_x2, V_z, T_a))))).
% 0.10/0.34 fof(cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0, axiom, ![V_a, V_b, V_c, T_a2]: (~class_Ring__and__Field_Opordered__semiring(T_a2) | (~c_lessequals(V_a, V_b, T_a2) | (~c_lessequals(c_0, V_c, T_a2) | c_lessequals(c_times(V_a, V_c, T_a2), c_times(V_b, V_c, T_a2), T_a2))))).
% 0.10/0.34 fof(cls_conjecture_3, negated_conjecture, c_lessequals(c_0, v_g(v_xa), t_b)).
% 0.10/0.34 fof(cls_conjecture_5, negated_conjecture, c_lessequals(c_HOL_Oabs(v_b(v_xa), t_b), c_times(v_ca, v_g(v_xa), t_b), t_b)).
% 0.10/0.34 fof(cls_conjecture_8, negated_conjecture, ~c_lessequals(c_HOL_Oabs(v_b(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), t_b)).
% 0.10/0.34 fof(clsrel_Ring__and__Field_Oordered__idom_33, axiom, ![T]: (~class_Ring__and__Field_Oordered__idom(T) | class_Orderings_Olinorder(T))).
% 0.10/0.34 fof(clsrel_Ring__and__Field_Oordered__idom_42, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_Ring__and__Field_Opordered__semiring(T2))).
% 0.10/0.34 fof(clsrel_Ring__and__Field_Oordered__idom_44, axiom, ![T2]: (~class_Ring__and__Field_Oordered__idom(T2) | class_Orderings_Oorder(T2))).
% 0.10/0.34 fof(tfree_tcs, negated_conjecture, class_Ring__and__Field_Oordered__idom(t_b)).
% 0.10/0.34
% 0.10/0.34 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.10/0.34 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.10/0.34 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.10/0.34 fresh(y, y, x1...xn) = u
% 0.10/0.34 C => fresh(s, t, x1...xn) = v
% 0.10/0.34 where fresh is a fresh function symbol and x1..xn are the free
% 0.10/0.34 variables of u and v.
% 0.10/0.34 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.10/0.34 input problem has no model of domain size 1).
% 0.10/0.34
% 0.10/0.34 The encoding turns the above axioms into the following unit equations and goals:
% 0.10/0.34
% 0.10/0.34 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.10/0.34 Axiom 2 (clsrel_Ring__and__Field_Oordered__idom_44): fresh(X, X, Y) = true.
% 0.10/0.34 Axiom 3 (clsrel_Ring__and__Field_Oordered__idom_33): fresh3(X, X, Y) = true.
% 0.10/0.34 Axiom 4 (clsrel_Ring__and__Field_Oordered__idom_42): fresh2(X, X, Y) = true.
% 0.10/0.34 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_44): fresh(class_Ring__and__Field_Oordered__idom(X), true, X) = class_Orderings_Oorder(X).
% 0.10/0.34 Axiom 6 (clsrel_Ring__and__Field_Oordered__idom_33): fresh3(class_Ring__and__Field_Oordered__idom(X), true, X) = class_Orderings_Olinorder(X).
% 0.10/0.34 Axiom 7 (clsrel_Ring__and__Field_Oordered__idom_42): fresh2(class_Ring__and__Field_Oordered__idom(X), true, X) = class_Ring__and__Field_Opordered__semiring(X).
% 0.10/0.34 Axiom 8 (cls_conjecture_3): c_lessequals(c_0, v_g(v_xa), t_b) = true.
% 0.10/0.34 Axiom 9 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh10(X, X, Y, Z, W) = true.
% 0.10/0.34 Axiom 10 (cls_Orderings_Ole__maxI2_0): fresh5(X, X, Y, Z, W) = true.
% 0.10/0.34 Axiom 11 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0): fresh8(X, X, Y, Z, W, V) = true.
% 0.10/0.34 Axiom 12 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh6(X, X, Y, Z, W, V) = c_lessequals(V, W, Y).
% 0.10/0.34 Axiom 13 (cls_Orderings_Ole__maxI2_0): fresh5(class_Orderings_Olinorder(X), true, X, Y, Z) = c_lessequals(Y, c_Orderings_Omax(Z, Y, X), X).
% 0.10/0.34 Axiom 14 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh9(X, X, Y, Z, W, V) = fresh10(c_lessequals(Z, W, Y), true, Y, W, V).
% 0.10/0.34 Axiom 15 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0): fresh7(X, X, Y, Z, W, V) = fresh8(c_lessequals(Z, V, Y), true, Y, Z, W, V).
% 0.10/0.34 Axiom 16 (cls_Orderings_Oorder__class_Oorder__trans_0): fresh9(class_Orderings_Oorder(X), true, X, Y, Z, W) = fresh6(c_lessequals(W, Y, X), true, X, Y, Z, W).
% 0.10/0.34 Axiom 17 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0): fresh7(class_Ring__and__Field_Opordered__semiring(X), true, X, Y, Z, W) = fresh4(c_lessequals(c_0, Z, X), true, X, Y, Z, W).
% 0.10/0.34 Axiom 18 (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).
% 0.10/0.35 Axiom 19 (cls_conjecture_5): c_lessequals(c_HOL_Oabs(v_b(v_xa), t_b), c_times(v_ca, v_g(v_xa), t_b), t_b) = true.
% 0.10/0.35
% 0.10/0.35 Goal 1 (cls_conjecture_8): c_lessequals(c_HOL_Oabs(v_b(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), t_b) = true.
% 0.10/0.35 Proof:
% 0.10/0.35 c_lessequals(c_HOL_Oabs(v_b(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), t_b)
% 0.10/0.35 = { by axiom 12 (cls_Orderings_Oorder__class_Oorder__trans_0) R->L }
% 0.10/0.35 fresh6(true, true, t_b, c_times(v_ca, v_g(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 19 (cls_conjecture_5) R->L }
% 0.10/0.35 fresh6(c_lessequals(c_HOL_Oabs(v_b(v_xa), t_b), c_times(v_ca, v_g(v_xa), t_b), t_b), true, t_b, c_times(v_ca, v_g(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 16 (cls_Orderings_Oorder__class_Oorder__trans_0) R->L }
% 0.10/0.35 fresh9(class_Orderings_Oorder(t_b), true, t_b, c_times(v_ca, v_g(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_44) R->L }
% 0.10/0.35 fresh9(fresh(class_Ring__and__Field_Oordered__idom(t_b), true, t_b), true, t_b, c_times(v_ca, v_g(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 1 (tfree_tcs) }
% 0.10/0.35 fresh9(fresh(true, true, t_b), true, t_b, c_times(v_ca, v_g(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 2 (clsrel_Ring__and__Field_Oordered__idom_44) }
% 0.10/0.35 fresh9(true, true, t_b, c_times(v_ca, v_g(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 14 (cls_Orderings_Oorder__class_Oorder__trans_0) }
% 0.10/0.35 fresh10(c_lessequals(c_times(v_ca, v_g(v_xa), t_b), c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), t_b), true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 18 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) R->L }
% 0.10/0.35 fresh10(fresh4(true, true, t_b, v_ca, v_g(v_xa), c_Orderings_Omax(v_c, v_ca, t_b)), true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 8 (cls_conjecture_3) R->L }
% 0.10/0.35 fresh10(fresh4(c_lessequals(c_0, v_g(v_xa), t_b), true, t_b, v_ca, v_g(v_xa), c_Orderings_Omax(v_c, v_ca, t_b)), true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 17 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) R->L }
% 0.10/0.35 fresh10(fresh7(class_Ring__and__Field_Opordered__semiring(t_b), true, t_b, v_ca, v_g(v_xa), c_Orderings_Omax(v_c, v_ca, t_b)), true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_42) R->L }
% 0.10/0.35 fresh10(fresh7(fresh2(class_Ring__and__Field_Oordered__idom(t_b), true, t_b), true, t_b, v_ca, v_g(v_xa), c_Orderings_Omax(v_c, v_ca, t_b)), true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 1 (tfree_tcs) }
% 0.10/0.35 fresh10(fresh7(fresh2(true, true, t_b), true, t_b, v_ca, v_g(v_xa), c_Orderings_Omax(v_c, v_ca, t_b)), true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_42) }
% 0.10/0.35 fresh10(fresh7(true, true, t_b, v_ca, v_g(v_xa), c_Orderings_Omax(v_c, v_ca, t_b)), true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 15 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) }
% 0.10/0.35 fresh10(fresh8(c_lessequals(v_ca, c_Orderings_Omax(v_c, v_ca, t_b), t_b), true, t_b, v_ca, v_g(v_xa), c_Orderings_Omax(v_c, v_ca, t_b)), true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 13 (cls_Orderings_Ole__maxI2_0) R->L }
% 0.10/0.35 fresh10(fresh8(fresh5(class_Orderings_Olinorder(t_b), true, t_b, v_ca, v_c), true, t_b, v_ca, v_g(v_xa), c_Orderings_Omax(v_c, v_ca, t_b)), true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_33) R->L }
% 0.10/0.35 fresh10(fresh8(fresh5(fresh3(class_Ring__and__Field_Oordered__idom(t_b), true, t_b), true, t_b, v_ca, v_c), true, t_b, v_ca, v_g(v_xa), c_Orderings_Omax(v_c, v_ca, t_b)), true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 1 (tfree_tcs) }
% 0.10/0.35 fresh10(fresh8(fresh5(fresh3(true, true, t_b), true, t_b, v_ca, v_c), true, t_b, v_ca, v_g(v_xa), c_Orderings_Omax(v_c, v_ca, t_b)), true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 3 (clsrel_Ring__and__Field_Oordered__idom_33) }
% 0.10/0.35 fresh10(fresh8(fresh5(true, true, t_b, v_ca, v_c), true, t_b, v_ca, v_g(v_xa), c_Orderings_Omax(v_c, v_ca, t_b)), true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 10 (cls_Orderings_Ole__maxI2_0) }
% 0.10/0.35 fresh10(fresh8(true, true, t_b, v_ca, v_g(v_xa), c_Orderings_Omax(v_c, v_ca, t_b)), true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 11 (cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) }
% 0.10/0.35 fresh10(true, true, t_b, c_times(c_Orderings_Omax(v_c, v_ca, t_b), v_g(v_xa), t_b), c_HOL_Oabs(v_b(v_xa), t_b))
% 0.10/0.35 = { by axiom 9 (cls_Orderings_Oorder__class_Oorder__trans_0) }
% 0.10/0.35 true
% 0.10/0.35 % SZS output end Proof
% 0.10/0.35
% 0.10/0.35 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------