%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 10:18:56 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.46s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:47:44 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.46 Command-line arguments: --no-flatten-goal
% 0.10/0.46
% 0.10/0.46 % SZS status Unsatisfiable
% 0.10/0.46
% 0.10/0.47 % SZS output start Proof
% 0.10/0.47 Axiom 1 (zero_is_smallest): less_equal(zero, X) = true.
% 0.10/0.47 Axiom 2 (x_divide_x_is_zero): quotient(X, X, zero) = true.
% 0.10/0.47 Axiom 3 (zero_divide_anything_is_zero): quotient(zero, X, zero) = true.
% 0.10/0.47 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.10/0.47 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.10/0.47 Axiom 6 (closure): quotient(X, Y, divide(X, Y)) = true.
% 0.10/0.47 Axiom 7 (divisor_existence): ifeq(quotient(X, Y, Z), true, less_equal(Z, X), true) = true.
% 0.10/0.47 Axiom 8 (less_equal_quotient): ifeq(quotient(X, Y, zero), true, less_equal(X, Y), true) = true.
% 0.10/0.47 Axiom 9 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 0.10/0.48 Axiom 10 (quotient_property): ifeq(quotient(X, Y, Z), true, ifeq(quotient(W, V, U), true, ifeq(quotient(T, V, Y), true, ifeq(quotient(S, V, X), true, ifeq(quotient(S, T, W), true, less_equal(Z, U), true), true), true), true), true) = true.
% 0.10/0.48
% 0.10/0.48 Goal 1 (prove_x_divde_zero_is_x): quotient(x, zero, x) = true.
% 0.10/0.48 Proof:
% 0.10/0.48 quotient(x, zero, x)
% 0.10/0.48 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(less_equal(x, divide(x, zero)), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 5 (ifeq_axiom) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(true, true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 6 (closure) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), divide(x, divide(x, zero))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(less_equal(divide(x, divide(x, zero)), zero), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 5 (ifeq_axiom) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(true, true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 6 (closure) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, divide(divide(x, divide(x, zero)), zero)), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(less_equal(divide(divide(x, divide(x, zero)), zero), zero), true, ifeq2(less_equal(zero, divide(divide(x, divide(x, zero)), zero)), true, zero, divide(divide(x, divide(x, zero)), zero)), divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 5 (ifeq_axiom) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(ifeq(true, true, less_equal(divide(divide(x, divide(x, zero)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(x, divide(x, zero)), zero)), true, zero, divide(divide(x, divide(x, zero)), zero)), divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 6 (closure) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, divide(x, zero)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(x, divide(x, zero)), zero)), true, zero, divide(divide(x, divide(x, zero)), zero)), divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 5 (ifeq_axiom) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(ifeq(true, true, ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, divide(x, zero)), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, divide(x, zero)), zero)), true, zero, divide(divide(x, divide(x, zero)), zero)), divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 6 (closure) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(ifeq(quotient(x, divide(x, zero), divide(x, divide(x, zero))), true, ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, divide(x, zero)), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, divide(x, zero)), zero)), true, zero, divide(divide(x, divide(x, zero)), zero)), divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 5 (ifeq_axiom) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(ifeq(true, true, ifeq(quotient(x, divide(x, zero), divide(x, divide(x, zero))), true, ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, divide(x, zero)), zero), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, divide(x, zero)), zero)), true, zero, divide(divide(x, divide(x, zero)), zero)), divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 6 (closure) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, divide(divide(x, divide(x, zero)), zero)), true, ifeq(quotient(x, divide(x, zero), divide(x, divide(x, zero))), true, ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, divide(x, zero)), zero), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, divide(x, zero)), zero)), true, zero, divide(divide(x, divide(x, zero)), zero)), divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 5 (ifeq_axiom) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, divide(divide(x, divide(x, zero)), zero)), true, ifeq(true, true, ifeq(quotient(x, divide(x, zero), divide(x, divide(x, zero))), true, ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, divide(x, zero)), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, divide(x, zero)), zero)), true, zero, divide(divide(x, divide(x, zero)), zero)), divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 3 (zero_divide_anything_is_zero) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, divide(divide(x, divide(x, zero)), zero)), true, ifeq(quotient(zero, divide(x, zero), zero), true, ifeq(quotient(x, divide(x, zero), divide(x, divide(x, zero))), true, ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, divide(x, zero)), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, divide(x, zero)), zero)), true, zero, divide(divide(x, divide(x, zero)), zero)), divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 5 (ifeq_axiom) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, divide(divide(x, divide(x, zero)), zero)), true, ifeq(true, true, ifeq(quotient(zero, divide(x, zero), zero), true, ifeq(quotient(x, divide(x, zero), divide(x, divide(x, zero))), true, ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, divide(x, zero)), zero), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, divide(x, zero)), zero)), true, zero, divide(divide(x, divide(x, zero)), zero)), divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 2 (x_divide_x_is_zero) R->L }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, divide(divide(x, divide(x, zero)), zero)), true, ifeq(quotient(divide(x, zero), divide(x, zero), zero), true, ifeq(quotient(zero, divide(x, zero), zero), true, ifeq(quotient(x, divide(x, zero), divide(x, divide(x, zero))), true, ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, divide(x, zero)), zero), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, divide(x, zero)), zero)), true, zero, divide(divide(x, divide(x, zero)), zero)), divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 10 (quotient_property) }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(x, divide(x, zero)), zero)), true, zero, divide(divide(x, divide(x, zero)), zero)), divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 4 (ifeq_axiom) }
% 0.10/0.48 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(less_equal(zero, divide(divide(x, divide(x, zero)), zero)), true, zero, divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.48 = { by axiom 1 (zero_is_smallest) }
% 0.10/0.49 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, ifeq2(true, true, zero, divide(divide(x, divide(x, zero)), zero))), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.49 = { by axiom 4 (ifeq_axiom) }
% 0.10/0.49 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(ifeq(quotient(divide(x, divide(x, zero)), zero, zero), true, less_equal(divide(x, divide(x, zero)), zero), true), true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.49 = { by axiom 8 (less_equal_quotient) }
% 0.10/0.49 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(true, true, ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero))), divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.49 = { by axiom 4 (ifeq_axiom) }
% 0.10/0.49 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(less_equal(zero, divide(x, divide(x, zero))), true, zero, divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.49 = { by axiom 1 (zero_is_smallest) }
% 0.10/0.49 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), ifeq2(true, true, zero, divide(x, divide(x, zero)))), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.49 = { by axiom 4 (ifeq_axiom) }
% 0.10/0.49 quotient(x, zero, ifeq2(ifeq(quotient(x, divide(x, zero), zero), true, less_equal(x, divide(x, zero)), true), true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.49 = { by axiom 8 (less_equal_quotient) }
% 0.10/0.49 quotient(x, zero, ifeq2(true, true, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x), x))
% 0.10/0.49 = { by axiom 4 (ifeq_axiom) }
% 0.10/0.49 quotient(x, zero, ifeq2(less_equal(divide(x, zero), x), true, divide(x, zero), x))
% 0.10/0.49 = { by axiom 5 (ifeq_axiom) R->L }
% 0.10/0.49 quotient(x, zero, ifeq2(ifeq(true, true, less_equal(divide(x, zero), x), true), true, divide(x, zero), x))
% 0.10/0.49 = { by axiom 6 (closure) R->L }
% 0.10/0.49 quotient(x, zero, ifeq2(ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(x, zero), x), true), true, divide(x, zero), x))
% 0.10/0.49 = { by axiom 7 (divisor_existence) }
% 0.10/0.49 quotient(x, zero, ifeq2(true, true, divide(x, zero), x))
% 0.10/0.49 = { by axiom 4 (ifeq_axiom) }
% 0.10/0.49 quotient(x, zero, divide(x, zero))
% 0.10/0.49 = { by axiom 6 (closure) }
% 0.10/0.49 true
% 0.10/0.49 % SZS output end Proof
% 0.10/0.49
% 0.10/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------