TSTP Solution File: SWV254-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV254-2 : 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 : Thu Aug 31 23:03:13 EDT 2023
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV254-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % 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 : 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 : Tue Aug 29 08:37:28 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.39 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.39
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 Take the following subset of the input axioms:
% 0.21/0.40 fof(cls_SetInterval_OatLeastLessThan__empty_0, axiom, ![T_a, V_n, V_m]: (~class_Orderings_Oorder(T_a) | (~c_lessequals(V_n, V_m, T_a) | c_SetInterval_OatLeastLessThan(V_m, V_n, T_a)=c_emptyset))).
% 0.21/0.40 fof(cls_SetInterval_OatLeastLessThan__singleton_0, axiom, ![V_m2]: c_SetInterval_OatLeastLessThan(V_m2, c_Suc(V_m2), tc_nat)=c_insert(V_m2, c_emptyset, tc_nat)).
% 0.21/0.40 fof(cls_Set_Oempty__not__insert_0, axiom, ![V_a, V_A, T_a2]: c_emptyset!=c_insert(V_a, V_A, T_a2)).
% 0.21/0.40 fof(cls_conjecture_0, negated_conjecture, ![V_U]: c_lessequals(V_U, v_x(V_U), tc_nat)).
% 0.21/0.40 fof(cls_conjecture_1, negated_conjecture, ![V_U2]: v_x(V_U2)=v_nat).
% 0.21/0.40 fof(clsarity_nat_3, axiom, class_Orderings_Oorder(tc_nat)).
% 0.21/0.40
% 0.21/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.40 fresh(y, y, x1...xn) = u
% 0.21/0.40 C => fresh(s, t, x1...xn) = v
% 0.21/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.40 variables of u and v.
% 0.21/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.40 input problem has no model of domain size 1).
% 0.21/0.40
% 0.21/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.40
% 0.21/0.40 Axiom 1 (clsarity_nat_3): class_Orderings_Oorder(tc_nat) = true2.
% 0.21/0.40 Axiom 2 (cls_conjecture_1): v_x(X) = v_nat.
% 0.21/0.40 Axiom 3 (cls_conjecture_0): c_lessequals(X, v_x(X), tc_nat) = true2.
% 0.21/0.40 Axiom 4 (cls_SetInterval_OatLeastLessThan__singleton_0): c_SetInterval_OatLeastLessThan(X, c_Suc(X), tc_nat) = c_insert(X, c_emptyset, tc_nat).
% 0.21/0.40 Axiom 5 (cls_SetInterval_OatLeastLessThan__empty_0): fresh(X, X, Y, Z, W) = c_SetInterval_OatLeastLessThan(W, Z, Y).
% 0.21/0.40 Axiom 6 (cls_SetInterval_OatLeastLessThan__empty_0): fresh2(X, X, Y, Z, W) = c_emptyset.
% 0.21/0.40 Axiom 7 (cls_SetInterval_OatLeastLessThan__empty_0): fresh(c_lessequals(X, Y, Z), true2, Z, X, Y) = fresh2(class_Orderings_Oorder(Z), true2, Z, X, Y).
% 0.21/0.40
% 0.21/0.40 Goal 1 (cls_Set_Oempty__not__insert_0): c_emptyset = c_insert(X, Y, Z).
% 0.21/0.40 The goal is true when:
% 0.21/0.40 X = v_nat
% 0.21/0.40 Y = c_emptyset
% 0.21/0.40 Z = tc_nat
% 0.21/0.40
% 0.21/0.40 Proof:
% 0.21/0.40 c_emptyset
% 0.21/0.40 = { by axiom 6 (cls_SetInterval_OatLeastLessThan__empty_0) R->L }
% 0.21/0.40 fresh2(true2, true2, tc_nat, c_Suc(v_nat), v_nat)
% 0.21/0.40 = { by axiom 1 (clsarity_nat_3) R->L }
% 0.21/0.40 fresh2(class_Orderings_Oorder(tc_nat), true2, tc_nat, c_Suc(v_nat), v_nat)
% 0.21/0.40 = { by axiom 7 (cls_SetInterval_OatLeastLessThan__empty_0) R->L }
% 0.21/0.40 fresh(c_lessequals(c_Suc(v_nat), v_nat, tc_nat), true2, tc_nat, c_Suc(v_nat), v_nat)
% 0.21/0.40 = { by axiom 2 (cls_conjecture_1) R->L }
% 0.21/0.40 fresh(c_lessequals(c_Suc(v_nat), v_x(c_Suc(v_nat)), tc_nat), true2, tc_nat, c_Suc(v_nat), v_nat)
% 0.21/0.40 = { by axiom 3 (cls_conjecture_0) }
% 0.21/0.40 fresh(true2, true2, tc_nat, c_Suc(v_nat), v_nat)
% 0.21/0.40 = { by axiom 5 (cls_SetInterval_OatLeastLessThan__empty_0) }
% 0.21/0.40 c_SetInterval_OatLeastLessThan(v_nat, c_Suc(v_nat), tc_nat)
% 0.21/0.40 = { by axiom 4 (cls_SetInterval_OatLeastLessThan__singleton_0) }
% 0.21/0.40 c_insert(v_nat, c_emptyset, tc_nat)
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40
% 0.21/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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