TSTP Solution File: ANA007-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ANA007-2 : 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 : n019.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 17:21:01 EDT 2023
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% 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 : ANA007-2 : 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
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 18:51:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.38 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.38
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 Take the following subset of the input axioms:
% 0.20/0.38 fof(cls_Orderings_Oorder__class_Oaxioms__1_0, axiom, ![T_a, V_x]: (~class_Orderings_Oorder(T_a) | c_lessequals(V_x, V_x, T_a))).
% 0.20/0.38 fof(cls_Ring__and__Field_Omult__cancel__right1_2, axiom, ![V_c, T_a2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | V_c=c_times(c_1, V_c, T_a2))).
% 0.20/0.38 fof(cls_conjecture_0, negated_conjecture, ![V_U]: ~c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)), t_b), c_times(V_U, c_HOL_Oabs(v_f(v_x(V_U)), t_b), t_b), t_b)).
% 0.20/0.38 fof(clsrel_Ring__and__Field_Oordered__idom_44, axiom, ![T]: (~class_Ring__and__Field_Oordered__idom(T) | class_Orderings_Oorder(T))).
% 0.20/0.38 fof(tfree_tcs, negated_conjecture, class_Ring__and__Field_Oordered__idom(t_b)).
% 0.20/0.38
% 0.20/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.38 fresh(y, y, x1...xn) = u
% 0.20/0.38 C => fresh(s, t, x1...xn) = v
% 0.20/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.38 variables of u and v.
% 0.20/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.38 input problem has no model of domain size 1).
% 0.20/0.38
% 0.20/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.38
% 0.20/0.38 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true2.
% 0.20/0.38 Axiom 2 (clsrel_Ring__and__Field_Oordered__idom_44): fresh3(X, X, Y) = true2.
% 0.20/0.38 Axiom 3 (cls_Ring__and__Field_Omult__cancel__right1_2): fresh(X, X, Y, Z) = Z.
% 0.20/0.38 Axiom 4 (clsrel_Ring__and__Field_Oordered__idom_44): fresh3(class_Ring__and__Field_Oordered__idom(X), true2, X) = class_Orderings_Oorder(X).
% 0.20/0.38 Axiom 5 (cls_Orderings_Oorder__class_Oaxioms__1_0): fresh2(X, X, Y, Z) = true2.
% 0.20/0.38 Axiom 6 (cls_Ring__and__Field_Omult__cancel__right1_2): fresh(class_Ring__and__Field_Oordered__idom(X), true2, X, Y) = c_times(c_1, Y, X).
% 0.20/0.38 Axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0): fresh2(class_Orderings_Oorder(X), true2, X, Y) = c_lessequals(Y, Y, X).
% 0.20/0.38
% 0.20/0.38 Goal 1 (cls_conjecture_0): c_lessequals(c_HOL_Oabs(v_f(v_x(X)), t_b), c_times(X, c_HOL_Oabs(v_f(v_x(X)), t_b), t_b), t_b) = true2.
% 0.20/0.38 The goal is true when:
% 0.20/0.38 X = c_1
% 0.20/0.38
% 0.20/0.38 Proof:
% 0.20/0.38 c_lessequals(c_HOL_Oabs(v_f(v_x(c_1)), t_b), c_times(c_1, c_HOL_Oabs(v_f(v_x(c_1)), t_b), t_b), t_b)
% 0.20/0.38 = { by axiom 6 (cls_Ring__and__Field_Omult__cancel__right1_2) R->L }
% 0.20/0.38 c_lessequals(c_HOL_Oabs(v_f(v_x(c_1)), t_b), fresh(class_Ring__and__Field_Oordered__idom(t_b), true2, t_b, c_HOL_Oabs(v_f(v_x(c_1)), t_b)), t_b)
% 0.20/0.38 = { by axiom 1 (tfree_tcs) }
% 0.20/0.38 c_lessequals(c_HOL_Oabs(v_f(v_x(c_1)), t_b), fresh(true2, true2, t_b, c_HOL_Oabs(v_f(v_x(c_1)), t_b)), t_b)
% 0.20/0.38 = { by axiom 3 (cls_Ring__and__Field_Omult__cancel__right1_2) }
% 0.20/0.38 c_lessequals(c_HOL_Oabs(v_f(v_x(c_1)), t_b), c_HOL_Oabs(v_f(v_x(c_1)), t_b), t_b)
% 0.20/0.38 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 0.20/0.38 fresh2(class_Orderings_Oorder(t_b), true2, t_b, c_HOL_Oabs(v_f(v_x(c_1)), t_b))
% 0.20/0.38 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_44) R->L }
% 0.20/0.38 fresh2(fresh3(class_Ring__and__Field_Oordered__idom(t_b), true2, t_b), true2, t_b, c_HOL_Oabs(v_f(v_x(c_1)), t_b))
% 0.20/0.38 = { by axiom 1 (tfree_tcs) }
% 0.20/0.38 fresh2(fresh3(true2, true2, t_b), true2, t_b, c_HOL_Oabs(v_f(v_x(c_1)), t_b))
% 0.20/0.38 = { by axiom 2 (clsrel_Ring__and__Field_Oordered__idom_44) }
% 0.20/0.38 fresh2(true2, true2, t_b, c_HOL_Oabs(v_f(v_x(c_1)), t_b))
% 0.20/0.38 = { by axiom 5 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 0.20/0.38 true2
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38
% 0.20/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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