%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWX186+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:45:31 PM UTC 2026
% Result : Theorem 0.10s 0.23s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX186+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n019.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Mon Sep 28 15:06:33 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.23 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.10/0.23
% 0.10/0.23 % SZS status Theorem
% 0.10/0.23
% 0.10/0.23 % SZS output start Proof
% 0.10/0.23 Axiom 1 (axiom_006): drop(s(X), nil) = nil.
% 0.10/0.23 Axiom 2 (axiom_007): drop(s(X), cons(Y, Z)) = drop(X, Z).
% 0.10/0.23 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.10/0.23 Axiom 4 (goal_009): ifeq(drop(X, Y), drop(X, Z), Y, Z) = Z.
% 0.10/0.23
% 0.10/0.23 Goal 1 (axiom_003): nil = cons(X, Y).
% 0.10/0.23 The goal is true when:
% 0.10/0.23 X = Y
% 0.10/0.23 Y = nil
% 0.10/0.23
% 0.10/0.23 Proof:
% 0.10/0.23 nil
% 0.10/0.23 = { by axiom 4 (goal_009) R->L }
% 0.10/0.23 ifeq(drop(s(s(X)), cons(Y, nil)), drop(s(s(X)), nil), cons(Y, nil), nil)
% 0.10/0.23 = { by axiom 1 (axiom_006) }
% 0.10/0.23 ifeq(drop(s(s(X)), cons(Y, nil)), nil, cons(Y, nil), nil)
% 0.10/0.23 = { by axiom 2 (axiom_007) }
% 0.10/0.23 ifeq(drop(s(X), nil), nil, cons(Y, nil), nil)
% 0.10/0.23 = { by axiom 1 (axiom_006) }
% 0.10/0.23 ifeq(nil, nil, cons(Y, nil), nil)
% 0.10/0.23 = { by axiom 3 (ifeq_axiom) }
% 0.10/0.23 cons(Y, nil)
% 0.10/0.23 % SZS output end Proof
% 0.10/0.23
% 0.10/0.23 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------