TSTP Solution File: SWV689-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV689-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n025.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 23:05:54 EDT 2023
% Result : Unsatisfiable 38.96s 5.43s
% Output : Proof 38.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV689-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 10:12:40 EDT 2023
% 0.20/0.35 % CPUTime :
% 38.96/5.43 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 38.96/5.43
% 38.96/5.43 % SZS status Unsatisfiable
% 38.96/5.43
% 38.96/5.43 % SZS output start Proof
% 38.96/5.43 Take the following subset of the input axioms:
% 38.96/5.43 fof(cls_assms_0, axiom, c_HOL_Oord__class_Oless(v_i, v_n, tc_nat)).
% 38.96/5.43 fof(cls_conjecture_0, negated_conjecture, ~c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i, v_k, tc_nat), v_n, tc_nat)).
% 38.96/5.43 fof(cls_less__imp__diff__less_0, axiom, ![V_n, V_j, V_k]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j, V_n, tc_nat), V_k, tc_nat) | ~c_HOL_Oord__class_Oless(V_j, V_k, tc_nat))).
% 38.96/5.43
% 38.96/5.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 38.96/5.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 38.96/5.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 38.96/5.43 fresh(y, y, x1...xn) = u
% 38.96/5.43 C => fresh(s, t, x1...xn) = v
% 38.96/5.43 where fresh is a fresh function symbol and x1..xn are the free
% 38.96/5.43 variables of u and v.
% 38.96/5.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 38.96/5.43 input problem has no model of domain size 1).
% 38.96/5.43
% 38.96/5.43 The encoding turns the above axioms into the following unit equations and goals:
% 38.96/5.43
% 38.96/5.43 Axiom 1 (cls_assms_0): c_HOL_Oord__class_Oless(v_i, v_n, tc_nat) = true2.
% 38.96/5.43 Axiom 2 (cls_less__imp__diff__less_0): fresh372(X, X, Y, Z, W) = true2.
% 38.96/5.43 Axiom 3 (cls_less__imp__diff__less_0): fresh372(c_HOL_Oord__class_Oless(X, Y, tc_nat), true2, X, Z, Y) = c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X, Z, tc_nat), Y, tc_nat).
% 38.96/5.43
% 38.96/5.43 Goal 1 (cls_conjecture_0): c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i, v_k, tc_nat), v_n, tc_nat) = true2.
% 38.96/5.43 Proof:
% 38.96/5.43 c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i, v_k, tc_nat), v_n, tc_nat)
% 38.96/5.43 = { by axiom 3 (cls_less__imp__diff__less_0) R->L }
% 38.96/5.43 fresh372(c_HOL_Oord__class_Oless(v_i, v_n, tc_nat), true2, v_i, v_k, v_n)
% 38.96/5.43 = { by axiom 1 (cls_assms_0) }
% 38.96/5.43 fresh372(true2, true2, v_i, v_k, v_n)
% 38.96/5.43 = { by axiom 2 (cls_less__imp__diff__less_0) }
% 38.96/5.43 true2
% 38.96/5.43 % SZS output end Proof
% 38.96/5.43
% 38.96/5.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------